CM1B Quiz
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Maseno University *
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Course
MAC
Subject
Finance
Date
Nov 24, 2024
Type
docx
Pages
60
Uploaded by CountOxideEchidna112
1B
01
0ws
i
e
Descriptive
data
analysis
The
question
spreadsheet
contains
data
on the €/€
exchange
rate
(ie
how
much
1
euro
s
worth
in
terms
of
pounds
sterling)for
each
day
i
2016,
A
descriptive
data
analyss
is
being
carried
outin
order
to
summaris
the
key
features
of
the
data
set
()
Determine:
(a)
the
highest
value
of
the €/€
exchange
rate
during
2016
and
the
date
on
which
this
occurred,
(b)
thelowest
value
ofthe
€/€
exchange
rate
during
2016
and
the
date
on
which
this
occured
(c)
the
average
value
of
the €/E
exchange
rate
for
2016.
(i)
Plota
graph
showing
the
€/¢
exchange
rate
each
day
during
2016,
including
a
ine
corresponding
to
the
average
exchange
rate
cakulated
in
().
i)
Calculate
the
number
of
days
during
2016
for
which
the
€/€
exchange
rate
s
in
each
of
the
following
ranges:
o
07000-07499
o
07500-07999
o
08000-084%9
o
08500-08999
+
0000-09499
CMIB0S:nterest
rates
Page1
i(p),
d(p),
d,
delta
(i)
Useaspreadsheet
to
calculate
the
values
of
i
(p=2,4,12),
¢
(p=2,4,12),
d
and
&
based
on
an
input
value
of
i
%
.
Express
your
answers
as
percentages
to
3DP.
(i)
Useaspreadsheet
to
calculate
the
values
of
i)
(p=2,4,12),
d)
(p=2,4,12),
&
and
i
based
on
an
input
value
of
d=1.4%.
Express
your
answers
as
percentages
to
30P.
CM1B05:
nterest
rates
Pager
Accumulated
values
Alump
sum
of
£100
is
invested
at
time
0.
()
Determine
the
accumulated
value
of
the
investment
at
time
t=1,2,
....
20
years
assuming
that
the
interest
rate
is
3.2%
pa
convertible
monthly.
(i)
Determine
the
accumulated
value
of
the
investment
at
time
t=1,2,
....
20
years
assuming
that
the
discount
rate
is
2.3%
pa
convertible
six-monthly.
(i)
Draw
a
single
graph
to
show
the
accumulated
values
of
the
investment
at
time
£=01,2,..,20
yearsat
an
interest
rate
of
4.5%
pa
effective
a
discount
rate
of
4.5%
pa
effective
an
interest
rate
of
4.75%
pa
convertible
quarterly
a
discount
rate
of
4%
pa
convertible
monthly
aforce
of
interest
of
4.9% pa.
CM1B.05:
nterest
rates
pager
Graphs
of
i(p)
and
d(p)
(i)
Draw
agraph
based
on
an
effective
interest
rate
of
4%
pa to
show
that
i”)
tends
towards
Saspon
(i)
Draw
a
graph based
on
an
effective
interest
rate
of
4%
pa
to
show
that
d') tends
towards
&
as
p—or
CM1B.05:
Interest
rates
Page1
Simple
and
effective
rates
of
interest
An
investment
of
£1,500
is
made
at
time
0
and
a
further
investment
of
£2,000
is
made
at
time
5.
The
investments
accumulate
at
a
simple
rate
of
interest
of
3%
pa.
Calculate
the
total
accumulated
value
at
the
end
of
every
year
for
the
next
10
years.
(i)
Determine
the
equivalent
annual
effective
rate
of
interest
earned
over
the
10
years
using
the
spreadsheet
you
created
in
part
(i)
and
the
GOALSEEK
function.
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CMIB.08:
Levl
annuites
page1
PV
and
AV
of
annuities
[0]
(i)
Use
a
spreadsheet
to
calculate
the
accumulated
value
at
time
12
of
an
annuity
paid
annually
in
advance
for
12
years
with
an
annual
payment
of
£150.
Use
i
=4%
pa
effective.
Demonstrate
the
value
obtained
using
year-on-year
accumulations
and
separately
using
an
annuity
formula.
Use
a
spreadsheet
to
calculate
the
present
value
at
time
0
of
an
annuity
of
payable
monthly
in
arrears
for
20
years
using
a
rate
of
interest
of
5% convertible
half-yearly,
where
the
annual
payment
under
the
annuity
is
£300.
OM18.08:Level
annuites
Page1
PV
of
annuities
(including
change
of
interest
rate)
[0]
(ii)
Payments
of
£550
are
made
at
times
6
to
15
years
inclusive.
The
effective
rate
of
discount
is
3%
pa.
Calculate
the
present
value
of
these
payments
at
time
0.
Repeat
the
calculations
in
part
(i)
assuming
that
the
rate
of
discount
is
now
3%
pa
from
time
0
to
time
10
and
3.5%
pa
thereafter.
(CMIB.08:
Level
annuities
page1
pthly
annuity
(as
p
increases)
Plot
a
graph
to
show
that
Amfi
(P=1,23,4,6,12,24)
tends
towards 400G75]
as
p—o
based
on
an
effective
interest
rate
of
4%
pa.
CM18.08:
Level
annuties
Page1
Equating
PVs
of
annuities
Determine
the
effective
annual
rate
of
interest
for
which
the
accumulated
value
at
time
8
of
an
‘annuity
which
pays
£500
at
the
end
of
every
six
months
in
years
1
to
8
inclusive
equals
the
present
value
at
time
8
of
an
annuity
which
pays
£900
annually
in
advance
in
years
9
to
18
inclusive.
CM1B.09:
Increasing
anntes
Page1
Present
value
of
increasing
annuities
Anincreasing
annuity
is
payable
annually
in
advance
for
10
years.
The
first
payment
is
100
Calculate
the
present
value
of
the
annuty
if:
(@)
paymentsincrease
by
20
each
year
(b)
paymentsincrease
by
5%
each
year.
You
should
assume
an
effective
annual
rate
of
interest
of
4%.
CM1B.09:Increasing
anntes
Page1
Balance
of
account
after
increasing
quarterly
withdrawals
Hollie
is
just
about
to
start
a
3-year
course
at
university
and
has
received
a
gift
of
£20,000
from
a
rich
relative.
She
invests
this
money
in
an
account
that
pays
interest
at
the
rate
of
3%
pa
effective.
The
account
allows
a
maximum
of
4
withdrawals
per
year.
Hollie
expects
to
make
withdrawals
at
the
end
of
each
quarter
while
she
is
at
university
(including
a
withdrawal
on
completion
of
her
course).
She
expects
her
first
withdrawal
to
be
£1,000,
and
that
withdrawals
will
increase
by
£100
each
quarter.
(i)
Using
the
above
assumptions,
calculate
the
balznce
of
Hollie's
account
at
the
end
of
her
course.
(i)
Calculate
the
amount
of
the
quarterly
increase
that
would
make
Hollie’s
balance
fall
to
zero
immediately
after
her
final
withdrawal.
CM18.09:
Increasing
annuities
Page
1
Deferred
annuity
with
variable
payments
A15-year
annuity
provides
annual
payments
with
the
first
payment
in
4
years’
time.
The
amount
of
the
first
payment
is
£5,000.
The
payment
amount
changes
over time
in
the
following
wa
.
Following
the
initial
payment
of
£5,000,
payments
increase
at
a
rate
of
3%
pa
compound.
«
Thereare
6
compound
increases
of
3%
in
total.
«
Thereare
noincreases
for
3
years
thereafter.
«
Theremaining
payments
decrease
at
a
rate
of
2%
pa
compound
In
the
calculations
sheet,
set
up
a
table
of
cashflows
and
calculate
the
present
value
of
this
annuity
using
a
rate
of
interest
of 7%
pa
effective.
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CM1B-10:
Equations
of
value
Page1
Solving
an
equation
of
value
to
find
the
interest
rate
In
return
for
an
investment
of
£100,000
on
12
June
2016,
an
investor
receives
the
following
cashflows:
|
Date
Cashflow
10ctober
2016
£18,000
31
December
2016
£25,000
[
1amay2017
£41,500
i
28
September
2017
£15,500
[
s
sanvary
2018
£8,000
Calculate
the
investor's
effective
annual
rate
of
return,
giving
your
answer
correct
to
the
nearest
0.1%.
CM1B-11:
Loan
schecules
page
Loan
schedule,
level
repayments
A
business
takes
out
a
bank
loan
of
50,000
to
be
repaid
by
level
quarterly
instalments
over
5
years.
The
annual
effective
interest
rate
on
the
loan
is
6%.
()
Calculate
the
amount
of
each
quarterly
repayment.
(i)
Setupaloan
schedule
that
includes:
.
the
amount
of
each
repayment
«
the
splitof
each
repayment
between
interest
and
capital
.
the
capital
outstanding
after
each
repayment
for
the
whole
term
of
the
loan.
(i)
Using
the
loan
schedule
from
part
(i),
determine:
(a)
the
total
amount
of
interest
paid
over
the
whole term
of
the
loan
(b)
theinterest
element
and
the
capital
element
of
the
7th
repayment
()
thetotal
interest
paid
and
capital
repaid
in
the
2nd
year.
Loan
schedule,
increasing
repayments
A
couple
takes
out
3
loan
of
40,000
to
purchase
a
yacht.
As
the
couple
have
a
low
current
Income,
but
are
expecting
their
income
to
grow
in
the
coming
years,
they
agree
to
make
monthly
repayments
in
arrears
for
15
years,
where
each
monthly
repayment
is
5
higher
than
the
previous
one.
The
annual
effective
interest
rate
on
the
loan
is
8%.
()
By
constructing
the
loan
schedule
for
the
whole
term
of
the
loan,
showing:
e«
theamount
of
each
repayment
©
thesplit
of
each
repayment
between
interest
and
capital,
and
©
the
capital
outstanding
after
each
repayment
calculate
the
amount
of
the
first
monthly
repayment
needed
to
ensure
that
the
capital
outstanding
is
0
at
the
end
of
the
term
of
the
loan.
(i)
Plota
graph
showing
the
capital
outstanding
at
the
end
of
each
year
of
the
15-year
term.
Comment
on
your
graph.
(v)
Determine
which
repayment
causes
the
capital
outstanding
to
fall
below
15,000,
CMIB
11
Lom
scheces
page1
APR
In
order
to
buy
some
new
bedroom
furniture,
a
woman
takes
out
a
loan
of
3,000,
Under
the
terms
of
the loan, the
repayment
schedule
is
as
follows:
©
norepayments
are
made
for
the
first
3
years
after
taking
out the
loan,
«
thenrepayments
of
250
are
made
quarterly
in
advance
for
the
next
2
years,
©
followed
by
repayments
of
450
quarterly
in
advance
for
the
next
3
years.
Calculate
the
APR
on
this
loan.
CM1312
Busines
project
apprasal
Paeet
Net
present
value
and
internal
rate
of
return
Malcolm,
an
aspiring
che,
i
intending
to
set
up
a
catering
business
to
sell
vegan
f0od
from
a
van
at
festivals.
The
purchase
price
of
the
van
is
20,000, and
Malcolm
estimates
that
he
will
incur
costs
of
3,000
monthly
in
arrears
for
1
year
from
the
date
of
purchase,
as
he
fits
out
the
van and
develops
his
range
of
products.
One
year
after
purchasing
the
van,
Macolm
expects
to
be
able
to
launch
his
business
and
start
selling
food.
He
estimates
that
his
net
income
from
his
first
year
of
sales
will
be
9,000,
and
that
this
figure
willincrease
by
4%
in
each
subsequent
year.
He
intends
to
work
all
year
round,
so
assumes
that
this
income
will
be
received
continuously.
Ten
years
after
purchasing
the
van,
Malcolm
wishes
to
retire,
and
he
believes
that
he
will
be
able
tosell
his
business
at
that
time
for
25,000.
()
Calculate
the net
present
value
of
the
project’s
cashflows,
assuming
an
interest
rate
of
7.2%
pa
effective.
)
Calculate
the
project’s
internal
rate
of
return.
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Comparing
projects
using
net
present
value
and
internal
rate
of
return
A
company
is
considering
investing
n
one
of
two
projects,
A
and
B.
The
cashfiows
forthe
two
projects
are
as
follows:
Project
&
«
inital
outgo
of
1,000,000
©
further
outgo
of
400,000
i the
midde
of
Year
1
«
income
of
500,000
recelved
at
the
end
of
Yeas
2
10
nclusive
Projects
«
intaloutgo
of
800,000
+
income
of
200,000
received
n
the
middie
of
Years
1
0’
inclusive
©
furtherincome
of
100,000t
the
end
of
Year
5
After
5
years,
both
projects
end and
there
are
no
further
cashfiows.
(3
Calculate
the
net
present
value
of
each
project
for
each
annual
effective
interest
rate
from
0%
to
1%
(inclusive),
using
steps
of
0.1%.
(6
Hence
plota
graph
showing
how
the
net
present
value
of
these
projects
varies
with
theinterest
rate
used
to
discount
the
cashflows.
(i)
Determine
the
interval
of
width
0.1%
in
which:
(3)
theinternalrate
of
return
for
Project
A
ies.
(6)
theinternal
rate
of
return
for
Project
B
ies.
(0
the
net
present
value
of
Project
Als
equal
to
the
net
present
value
of
Project
8.
Discounted
payback
period
and
payback
period
An
employer
is
considering
sending
an
employee
on
a
training
course
in
order
to
develop
new
skl
and
5o
be
more
productive
to
the
company.
However,
the
employer
i
concemed
about
the
costs
involved
and,
in
particular,
the
rsk
that
the
employee
willleave
before
the
company
has
recouped
these
costs
through
additional
income
generated
by
the
employee's
work.
The
training
course
lasts
for
2
years
and
costs
3,000
per
quarter,
payable
in
advance
to
the
training
provider.
In
addition,
Guring
the
2-year
course,
the
employer
will need
to
allow
the
‘employee
time
off
for
study
and
exam
leave,
costing
the
employer
20,000
per
year
in
lost
productivity,
incurred
in
equal
instalments
quarterly
in
arrears.
10
the
first
year
ater
the
course
is
complted,
the
employee
will
generate
total
additional
revenue
of
30,000,
received
in
equal
instalments
quarterly
n
arrears.
This
figure
will
increase
by
4%
in
each
subsequent
year.
Once
the
employee
has
completed
the
course,
the
employer
will
need
to
increase
the
employee's
remuneration.
In
thefirst year
after
the
course
is
completed,
the
employer
will
eed
1o
pay
the
‘employee
a
total
addtional
alary
of
10,000,
payable
in
equal
instaiments
quarterly
n
arrears,
‘and
an
additional
bonus
of
1,500
2t
the
end
of
the
year.
The
additional
saary and
bonus
are
expected
to
increase
by
2%
n
each
subsequent
year.
Assuming
that
the
employee
remains
with
the
company,
calculate:
()
the
discounted
payback
period
of
the
cashflows
associated
with
the
employee
attending,
the
training
course
using
an
annual
effective
interest
rate
of
7%
)
the
payback
period.
Accumulated
profit
The
organisers
of
an
intemational
tennis
tournament
are
planning
to
build
a
new
stadium
in
their
grounds
to
accommodate
additonal
spectators
and
improve
tlevision
coverage
of
the
even.
The
stadium
will
take
3
years
to
buil.
The
buding
costs
will
be
6
millio
inthe
first
year
of
construction,
millon
in
the
second
year,
and
12
millon
i
the
third
year.
The
construction
costs
are
assumed
to
be
incurred
monthly
i
arrears.
Construction
i
scheduled
to
begin
on
1
July
2020,
50
that
the
new
stadium
willbe
completed
and
readyfor
use
on
1
uly
2023
The
tennis
tournament
is
held
each
year
inJuly,
and
the
additional
et
income
received
at
the
end
of
uly
2023252
resultof
the
new
stadiumIs
estimated
to
be
5,75
million.
The
additionalnet
Income
received
a
the
end
of
July
2024
i
estimated
1o
be
6.5
millon,
with
an
increase
of
.75
mitlon
expected
in
each
subsequent
year.
I
other
months
during
the
year,
when
the
new
stadium
is
ot
used
for
the
tournament,
the
maintenance
cost
s
assumed
to
be
0.05
million,
incurred
atthe
end
of
each
month,
with
the
first
such
costincurred
atthe
end
of
August
2023
I
order
to
fund
the
stacium's
construction,
the
tournament
organisers
ntend
to
take
out
an
interest.onl
loan
of
33
millon.
At
the
end
of
each
month,
the
organisers
must
pay
interest
on
the
loan
amount,calculated
using
a
monthly
effectiveinterest
rate
o
1%.
The
loan
must
be
repaid
in
full
aiter
10
years,
with
no
early
repayment
option.
The
33
million
from
the
oan
wil
b
received
on
1
July
2020
and
placed
in
2
bank
account
that
pays
interest
at
a
rate
of
0.85%
per
month
effective.
Al
cashflows
associated
with
the
project
re
paid
nto,
or
out
o,
this
bank
account.
By
projecting
the
balance
of
this
bank
account,calculate
the
accumulated
profit
of
the
new
stadium
for
the
toumament
organisers
on
1
uly
2030,
after
the
loan
has
been
repaid
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Price
of
a
property
An
investor
is
considering
buying
a
property
with
the
intention
of
renting
it
out.
Rent
will
be
payable
monthly
in
advance,
with
the
first
payment
expected
to
be
recerved
exactly
3
months
after
the
purchase
date.
The
initial
level
of
rental
income
is
expected
to
be
£800
per
month.
Rent
is
expected
to
increase
at
two-yearly
intervals
at
the
rate
of
1.5%
pa
compound.
After
letting
the
property
for
10
years,
the
investor
intends
to
sell
it
and
expects
to
achieve
a
sale
price
of
£500,000.
Construct
a
schedule
of
income
payments
and
hence
calculate
the
price
the
investor
should
pay
1o
achieve
a
rate
of
return
of
5%
pa
effective.
CM1313:Bonds
equiyand
property
[
Fixed-interest
security
A
fixed-interest
security
was
issued
on
1
January
in
a
given
year.
The
security
pays
coupons
of
4%
pa half-yearly
in
arrears.
It
is
redeemable
5
years
after
issue
at
the
rate
of
102%
and
has
a
8ross
redemption
yield
of
4.5%.
An
investor
buys
£10,000 nominal
of
the
security
on
the
issue
Gate.
The
investor
is
subject
to
tax
on
income
at
the
rate
of
40%
and
tax
on
capital
gains
at
the
rate
of
25%.
Income
tax
is
paid
on
coupons
at
the
end
of
the
calendar
year
in
which
the
coupon
is
received.
Capital
gains
tax
is
paid
immediately
on
sale
o
redemption.
()
Inanew
sheet
named
‘Price’,
calculate
the
price
at
issue
of
£10,000
nominal
of
the
security.
Three
years
after
buying
the
security,
the
investors
rate
of
income
tax
increases
to
41%.
(i)
Inanew
sheet
named
‘Cashflows',
create
a
schedule
of
the
investor’s
net
income
payments
assuming
that
the
bond
is
held
until
redemption.
i)
Inanew
sheet
named
"Yield',
calculate
the
effective
net
yield
earned
by
the
investor
as
a
result
of
holding
this
security
unti
the
redemption
date.
You should
give
your
answer
to
the
nearest
0.1%.
CM18-13:
Bonds,
equityand
propety
page1
Fixed-interest
security
with
optional
redemption
date
A
fixed-interest
security
pays
coupons
of
6%
po
annually
in
arrears.
Capital
is
to
be
redeemed
at
par
on
a
coupon
date
between
5
and
10
years
(inclusive)
after
the
issue
date.
The
date
of
redemption
is
at
the
option
of
the
borrower.
Aninvestor,
who
is
subject
to
income
tax
at
the
rate
of
20%
but
is
not
subject
to
capital
gains
tax,
purchases
the
security
on
the
issue
date.
()
Create
a
schedule
of
the
cashfiows
that
the
investor
will
receive
per
£100
nominal
of
the
stock
assuming
that
it
s
redeemed
at
the
earfiest
possible
redemption
date,
and
calculate
the
total
present
value
of
these
cashflows
using
an
interest
rate
of
5%
pa
effective.
(i)
Extend
the
schedule
in
part
()
to
calculate
the
present
value
of
the
investor's
cashflows.
for
each
possible
redemption
date
using
an
interest
rate
of
5%
po
effective.
(i)
State
with
reasons
the
maximum
price
the
investor
should
pay
per
£100
nominal
in
order
10
obtain
a
net
yield
of
at
least
5%
pa
effective.
Real
and
money
rates
of
return
An
investor
bought
1,000
shares
at
a
price
of
432p
per
share
on
1
July
2014
and
sold
the
shares
for
486p
each
on
30
June
2018
jus
after
receving
a
dvidend.
The
following
dvidends
were
paid
on
30
June
each
year
30June
inyear
Dividend
per
share
(5)
2015
161
2016
164
2017
0
2018
s
These
values
are
given
n
the
question
spreadsheet
for
this
unt
(along
with
the
values
of
the
price
index
referred
toin
pat
(1)
below).
()
Construct
aschedule
showing
the
investor's
cashflows
and
hence
calculte
the
money.
rate
of
return
achieved
by
the
investor.
The
values
of
the
retai
price
Index
on
each
30
June
between
2014
and
2018
were
asfollows
30June
inyear
Retai
price
index
2014
1ma
2015
1256
2016
1290
2007
1m7
208
1368
(i)
Using
the
retal
price
index
values
shown
n
the
table,
calculte
the
real
rate
of
return
per
annum
effective
achieved
by
the
investor.
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CM18-13:
Bonds,
equiyand
property
[
Index-linked
bond
In
March
2010,
the
government
of
country
issued
an
index-inked
bond
with
a
term
of
6
years.
Coupons
were
payable
half-yearly
in
arrears
at
the
nominal
rate
of
2.5%
po.
The
nominal
redemption
rate
was
100%.
Interest
and
capital
payments
were
linked
to
the
value
of
an
inflation
index
with
a
time
lag
of
2
months.
Atax-exempt
investor
purchased
£10,000 nominal
atissue
and
held
it
to
redemption.
The
issue
price
was
£96.50
per
£100
nominal
Values
of
the
inflation
index
are
given
in
the
question
spreadsheet
for
this
unit.
()
Construct
a
schedule
of
the
investor's
cashflows,
showing
the
amount
and
month
of
each
cashfiow.
Determine
the
annual
effective
real
yield
obtained
by
the
investor
to
the
nearest
0.1%.
€181
Term
st
o
et
rtes
[
Spot
rates,
forward
rates
and
par
yield
An
economist
believes
that
the
n-year
spot
rate,
,
,
wil
be
given
by
the
formula:
Va=003+0.020-000150%
forn=
0
over
the
next
10
years
()
(@)
Calulate
the
spot
fates
yy
Vameu¥io
(b)
Plota
graph
of
these
spot
rates
The
1-year
forward
rate
applying
from
time
¢
to
time
¢+1
is
denoted
by
f;
i
(a)
Calculate
the
1-year
forward
rates
fo,
f,
...,
fy
implied
by
the
spot
rate
formula,
()
Plota
graph
of
these
forward
rates.
A
10-year
fixed-interest
bond
pays
coupons
annually
in
arrears.
The
coupon
rate
is
4%
pa
for
the
first
5
years
and
6%
pa
for
the
following
5
years.
The
redemption
rate
is
110%.
(i)
(a)
Calculate
the
price
for
100
nominal
of
this
bond.
(b)
Hence
calculate
the
bond's
gross
redemption
yield.
()
Calculate
the
8-year
par
yield.
M8
14
Term
st
o
ot
rtes
[
Discounted
mean
term
and
convexity
A
company
has
a
liability
to
make
payments
at
the
end
of
each
year
for
the
next
40
years.
The
annual
payment
s
100,000
for
the
first
4
years,
and
at
the
end
of
each
4-year period
the
annual
payment
amount
is
expected
to
increase
by
10%.
The
annual
effective
interest
rate
is
5%
for
the
whole
of
the
period.
Calculate:
(3)
the
total
present
value
(b)
the
discounted
mean
term
(OMT),
and
(9
the
convexity
of
the
company's
liability
cashflows.
‘The
company
revises
s
assumption
on
the
4-yearly
increase
factor
from
10%
to
15%.
Calculate
the
revised
DMT.
(i)
Explain
why
the
DMT
has
changed
in
the way
that
it
has
done.
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M8
14
Term
st
o
ot
rtes
Page1
Immunisation
A
company
must
make
payments
at
time
¢
of:
for
£=5,6,7,
50,000+
750(t
-5)
0
years.
Galculae:
o
thetotal
present
value
o
thevolatity,
and
o
theconverty
of
the
payments
the
company
must
make,
assuming
that
the
annual
effective
interest
rate
s
2:5%
for
the
whole
of
the
period.
n
order
to
meet
s
labilties,
the
company
is
considering
purchasing
884,200 nominal
of
a
12.26-year
zero-coupon
bond.
(i)
(i)
™
Calcuiate:
o
thepresentvalve
o
thevolatity,
and
o
the
convexity
of
the
zero-coupon
bond
payment,
again
assuming
that
the
annual
effective
interest
rate
s
2:5%
for
the
whole
of
the
period.
Calculate
the
difference
in
value
between
the
present
value
of
the
asset
cashflow
(ie
that
from
the
zero-coupon
bond)
and
the
present
value
of
the
liability
cashflows
if
the
interest
rate
changes
immediately
to:
@
2%
()
3%
Explain
your
results
to
in
the
context
of
Redington's
conditions
for
immunisation.
1815
The
Lt
Tae
paeet
Ultimate
mortality
table
Use
the
question
spreadsheet
to
answer
the
following
question.
(i)
(i)
(iv)
On
the
‘Life
Table’
tab,
calculate
AM92
Ultimate
I,
and
d,
values
for
ages
X=17,18,...120,
using the
Ultimate
mortality
probabilities
given
on
the
‘Mortality
rates’
tab,
and
having
a
radix
of
Iy,
=10,000
Inthe
ife
table
worksheet
constructed
in
part
(i),
add
a
further
column
showing
the
force
of
mortality
over
each
integer
year
of
age
[x,
x+1],
assuming
the force
of
mortality
is
constant
over
each
year
of
age
Use
the
life
table
constructed
in
part
()
to
calculate
the
following
values:
@
sh
R
©
e
©
e
Copy
your
spreadsheet
from
part
(i)
onto
a
new
tab
and
adapt
the
e
table
5o
that
it
reflects
the
following mortality
basis:
4,
=08g/M2
where:
M52
=
mortalty
rate
from
the
AM92
Ultimate
table
Hence
recalculate
the
values
in
part
(i)
on
the
revised
basis.
1815
The
Lt
Tae
[
Select
mortality
table
Use
the
question
spreadsheet
to
answer
the
following
question.
()
Onthe
Life
Table’tab,
in
the
relevant
column
calculate
AMO2
Select
.31
values
for
ages
x=18,19,..91,
using
the
given
Ultimate
Iy
values
and
the
relevant
mortaity
probabiltiesfrom
the
Mortaiy
rates’tab.
(i)
Using
the
hyy}.q
and
I,
values,
in
the
relevant
column
calculate
the
associated
values
of
L
Calculate
AM92
Select
f
and
dy,)
values
in
a
similar
way
to
parts
()
and
(i),
for
ages
Xx=17,19,..90.
(iv)
Use
the
select
ife
table
constructed
in
part
()
to
calculate
the
probabilties
of
the
following
events:
(a)
@
select
lfe
currently
aged
exactly
64
i
stillalive
five
years
later
(b)
alife
who
was
selected
one
year
ago
when
aged
exactly
45,
dies
within
the
next
18years
()
alifeaged
exactly
41,
who
was
selected
one
year
ago,
is
stil
live
in
9
years’
time
butis
dead
by
age
57
(@)
aselect
life
who
s
currently
aged
exactly
63
dies
in
the
coming
year
(e)
aselect
life
who
s
currently
aged
exactly
63
dies
between
exact
ages
64
and
65
()
aselectlife
who
s
currently
aged
exactly
63
dies
between
exact
ages
65
and
66.
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Temporary
annuities
Use
the
question
spreadsheet
to
answer
the
following
question.
Use
the
mortality functions
on
the
‘Life
Table'
tab
where
appropriate.
i)
i)
0na
new
tab,
calculate
the
expected
present
value
(EPV)
of
level
temporary immediate
annuity,
paying
100
at
the
end
of
each
year
for
15
years
or
unti
the
earler
death
of
alife
currently
aged
exactly
62
n
order
to
perform
the
calculation,
create
columns
showing:
(1)
the
amount
of
payment
made
in
year
t
(2)
the
amount
by
which
that
payment
is
discounted
(3)
the
probability
of
the
payment
being made.
‘The
interest
rate
should
be an
input
variable.
Basis:
AMS92
Ultimate
Interest:
3%
pa
effective
Use
the
spreadsheet
in
part
(i)
to
calculate
the
EPV
of
the
following
temporary immediate
annuities
(all
with
payments
at
the
end
of
each
year
for
15
years
or
untilthe
death
of
(62),
if
eariier),
and
using
the
same
mortality
and
interest
basis:
(3
first
payment
of
100,
increasing
by
a
level
amount
of
10
each
year
(o)
first
payment
of
100,
increasing
by
2%
pa
compound
()
level
payments
of
100
for
ten
years,
followed
by
payments
of
300
for
the
remaining
five
years.
Recalculate
the
value
of
the
level
temporary
annuity
in
part
()
usi
4%
po
effective.
an
interest
rate
of
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(i)
Term
assurances.
Use
the
question
spreadsheet
to
answer
the
following
question.
Use
the
mortality functions
on
the
‘Life
Table'
tab
where
appropriate.
On
a
new
tab,
calculate
the
expected
present
value (EPV)
of
a
15-year
level
term
assurance,
paying
100,000
at
the
end
of
the
year
of
death
of
a
lfe
currently
aged
exactly
47.
As
part
of
your
calculation,
reate
three
columns
showing:
(1)
the
amount
of
payment
made
in
year
t
(2)
the
amount
by
which
that
payment
is
discounted
(3)
the
probability
of
the
payment
being made.
Basis:
AMS92
Select
Interest:
2%
pa
effective
Copy
the
spreadsheet
from
part
(i)
as
required,
and
adapt
it
to
calculate
the
EPV
of
each
of
the
following
term
assurances
(all
with
payments
at
the
end
of
the
year
of
death
of
a
select
ife
currently
aged
47
exact,
within
a
term
of
15
years),
and
using
the
same.
mortalty
and
interest
basis:
()
150,000
on
death
in
the
first
year,
decreasing
by
a
level
amount
of
10,000
each
Year
(50
the
benefit
on
death
in
the
final
year
is
10,000)
()
first
payment
of
75,000,
increasing
by
3%
pa
compound
(@)
the
amount
on
death
i
equal
to
the
amount
of
capital
outstanding
at
the
start
of
the
year
of
death,
on
a
15-year
mortgage
of
150,000
serviced
by
level
annual
repayments
(made
in
arrear)
at
a
mortgage
interest
rate
of
4%
pa
effective.
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Endowment
assurances
Use
the
question
spreadsheet
to
answer
the
following
question.
Use
the
mortality functions
on
the
‘Life
Table'
tab
where
appropriate.
(i)
On
a
new
tab,
calculate
the
expected
present
value (EPV)
of
a
20-year
endowment
assurance,
paying
50,000
immediately
on
death
of
a
life
currently
aged
exactly
36.
In
order
to
perform
the
calculation,
create
three
columns
showing,
for
each
of
the
20
possible
years
of
death,
and
for
the
year
of
maturity
separately:
(1)
the
amount
of
benefit
payment
each
year
(2)
the
amount
by
which
that
payment
is
discounted
(3)
the
probability
of
the
payment
being
made.
Basis
Mortality:
AM92
Select
Interest:
3.5%
pa
effective
Copy
the
spreadsheet
from
part
()
as
required,
and adapt
it
to
calculate
the
EPV
of
each
of
the
following
with-profits
endowment
assurances,
assuming
the
same
mortality
and
interest
basis.
Each
contract
has
a
basic
sum
assured
of
50,000,
a
term
of
20
years,
with
the
sum
assured
and
bonuses
payable
on
survival
to
the
end
of
the
term
or
immediately
on
earlier
death
of
(36).
()
Simple
reversionary
bonus
of
2%
pa
vesting
in
full
at
the
start
of
each
year.
No
terminal
bonus.
(b)
Simple
reversionary
bonus
of
2%
pa
vesting
in
full
at
the
end
of
each
year,
plus
a
terminal
bonus
equal
to
40%
of
the
reversionary
bonuses
attaching
at
the
time
of
claim.
(@)
Compound
bonus
of
1.25%
pa,
vesting
in
full
at
the
end
of
each
year,
plus
a
terminal
bonus
equal
to
2xt%
of
the
sum
assured
and
reversionary
bonuses
attaching
at
the
time
of
claim,
where
t
is
the
exact
duration
of
the
policy
(including
any
fractions
of
a
year)
at
the
time
of
claim.
(@)
As(c)
except
that,
after
10
years,
the
reversionary
bonus
is
assumed
o
reduce
to
arate
of
1% pa
compound,
and
the
terminal
bonus
rate
reduces
to
1.75x%
.
The
first
reversionary
bonus
to
be
declared
at
the
new
rate
is
the
one
declared
at
the
end
of
the
tenth
year
le
at
exact
duration
10),
and
the
new
revised
terminal
bonus
rate
applies
to
all
death
and
maturity
benefits
payable
after
time
10,
(e)
Super-compound
bonus
at
rates
of
1%
pa
of
the
sum
assured
and
4%
pa
of
the
attaching
bonuses.
Bonus
vests
in
full
at
the
end
of
each
year.
No terminal
bonus,
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€132
Gross
premiums
paeet
Endowment
assurance
Use
the
question
spreadsheet
to
answer
the
following
question.
Use
the
mortality
functions
on
the
‘Lfe
Table’
tab
where
appropriate.
An
endowment
assurance
with
an
18-year
term
will
pay
a
sum
assured
of
75,000
at
the
end
of
the
term,
or
at
the
end
of
the
year
of
death
of
a
ife
currently
aged
exactly
37,
if
earler.
Level
annual
premiums
are
payable
at
the
start
of
each
year
whille
the
policy
is
in
force.
‘The
insurance
company
uses
the
following
basis
for
the
calculation
of
gross
premiums:
Mortality:
AM92
Ultimate
Interest:
3%
pa
effective
Expenses
nital
05%of
the
sum
assured
Renewal:
38
pa
payable
at
the
start
of
each
year
except
the
first
Claim
350
paid
at
the
time
of
claim
(either
on
death
or
maturity)
Commission
Initial:
20%
of
the
first
annual
premium
Renewal:
2%
of
each
subsequent
annual
premium
(i
paid
at
the
start
of
each
year
except
the
first)
()
Calculate
the
gross
annual
premium
for
the
contrac.
Hint:
make
the
interest
rate
and
the
premium
input
variables
in
your
spreadsheet.
(i)
Recalculate
the
premium
assuming
the
effective
interest
rate
is
(2)
2%
pa
and
(b)
4%
po.
Give
a
brief
explanation
of
the
results
obtained.
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With-profits
gross
premium
Use
the
question
spreadsheet
to
answer
the
following
question.
Use
the
mortalty
functions
on
the
‘U
Table’
tab
where
appropriate.
Awith-profits
endowment
assurance
with
a
20-year
termis
to
be
ssued
10
a
fe
aged
exactly
42.
The
basic
sum
assured
willbe
56,000,
and
the
company
expects
to
declare
simple
reversionary
bonuses
of
2%
of
the
sum
assured
each
year.
Bonuses
wilvest
at
the
end
of
each
year,
and
the
sum
assured
plus
al
declared
bonuses
wil
be
paid out
at
the
end
of
the
term
or
immediately
on
earier
death.
The
contract
will
be
subject
o
level
annual
premiums
payable
at
the
start
of
each
year.
The
insurance
company
uses
the
following
basisfor
the
caculation
of
s
premiums:
Moraliy:
AM92
Select
Interest:
3%
po
effective
00
Payable
a
the
stat
of
each
year
except
the
first,
beginning
at
the
level
o
40 a
the
start
of
year
2
and
nflating
at
the
rate
of
15%
po
thereatter.
claim:
The current
rates
are
200
on
death
and 300
on
maturity.
These
amounts
are
assumed
1o
infate
at
the
rate
of
1.5%
pa
from
the
policyinception
date.
Expenses
Commission
nita
25%
of
the
first
annual
premium
Renewal:
1%
of
each
subsequent
annual
premium
ie paid
at
the
start
of
each
year
except
the
firs)
Calculate
the
gross
annual
premium
for
the
contract
Hint:
make
the
premium
on input
voriable
in
your
spreadsheet.
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Level
temporary
annuity
Use
the
question
spreadsheet
to
answer
the
following
question.
Use
the
mortality functions
provided.
Atemporary
immediate
annuity-due
with
a
15-year
term
makes
level
payments
of
10,000
po.
Payments
will
be
made
for
the
whole
15
years
or until
the
death
of
the
policyholder,
if
earier.
The
policyholder
s
aged
exactly
65
at
outset.
‘The
insurance
company
uses
a
prospective
formula
and
the
following
basis
for
the
calculation
of
its
premiums
and
reserves:
Mortality:
PMA92C20
Interest:
3%
pa
effective
Initial
expenses:
500
Regular
expenses:
25
paid
at
the
start
of
each
year
except
the
first
()
intab
(),
the
column
headed
‘EPV*
s
already
populated
with
values
of
the
form:
V'
epes
Where
¢
isthe
time
at
which
the
payment
is
made.
(a)
Using
this
column
of
values,
or
otherwise,
populate
the
column headed
‘annuity-
due
factor”
with
values
of
the
form:
Clcurent
age)
fremaing
erm]|
(o)
Calculate
the
prospective
gross
premium
reserve
for
this
policy
at
each
policy
duration
from
0
to
14
inclusive
(noting
that
the
reserve
at
duration
0
i
calculated
immediately
before
the
premium
and
expense
that
are
due
at
that
time).
Assume
for
this
purpose
that
the
single
premium
is
100,000.
You
may
use
the
annuity
factors
from
part
()
or
any
other
suitable
method.
()
Calculate
the
single
premium
(to
the
nearest
whole
unit)
that
will
make
the
prospective
reserve
at
duration
0
equal
to
zero.
(@)
Plotagraph
of
the
resulting
reserves
at
each
duration.
(e)
Describe
and
briefly
explain
the
pattern
of
reserve
values
you
have
calculated.
(i)
Recalculate
the
reserves
(and
plot
the
graph)
assuming
an
interest
rate
of
2.5%
pa
instead
of
3%
pa.
The
single
premium
should
be
kept
the
same
as
before.
Describe
and
briefly
explain
the
impact
that
this
change
in
the
interest
assumption
has
on
the
reserves.
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18
21:
Reseves
page1
Retrospective
accumulations
Use
the
question
spreadsheet
to
answer
the
following
question.
Use
the
mortality functions
provided.
The
insurance
company
uses
the
following
basis
to
calculate
retrospective
accumulations:
Mortality:
PMA92C20
Interest:
3%
pa
effective
Aman
aged
exactly
65
is
considering
taking
out
some
kind
of
lfe
insurance
policy.
1]
i)
(i)
()
Under
one
type
of
policy,
premiums
of
1,000
pa
will
be
paid
for
15
years
or
until
the
man's
death,
if
this
occurs
sooner.
On
tab
(i)
calculate
the
retrospective
accumulation
of
these
premiums
at
the
end
of
the
policy
term.
The
man
is
considering
taking
out
a
term
assurance
policy,
under
which
a
benefit
of
10,000
will
be
paid
immediately
on
his
death,
f
this
occurs
within
the
next
15
years
only.
Calculate
the
retrospective
accumulation
of
these
benefit
payments
at
the
end
of
the
policy
term.
The
man
i
also
considering
whether
to
take
out
a
full
endowment
assurance,
which
will
pay
10,000
at
the
end
of
the
15
year
term
or
immediately
on
earlier
death.
Calculate
the
retrospective
accumulation
of
these
benefit
payments
at
the
end
of
the
policy
term.
Recalculate
part
(i)
assuming
an
interest
rate
of
4%
po,
and
explain
the
answer
you
obtain.
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Endowment
assurance
Use
the
question
spreadsheet
to
answer
the
following
question.
Use
the
mortalty
functions
on
the
‘U
Table’
tab
where
appropriate.
An
endowment
assurance
with
an
18-year
term
has
a
sum
assured
of
75,000,
which
is
payable
at
the
end
of
the
term
or
immediately
on
ealier
death.
The
policyholder
was
aged
exacty
37
at
entry.
Level
annual
premiums
of
3,380
are
payable
at
the
startof
each
year.
The
insurance
company
uses
a
prospective
formula
and
the
folowing
basis
for
the
calculation
of
its
reserves:
Mortaly:
AM92
Ultimate
nterest
2%
pa
effective
Inital
expenses
500
Regular
expenses:
40
paid
at
the
start
of
each
year
exclucing
the
first
Inital
commission:
20%
of
the
frst
year's
premium
Renewal
commission:
2.5%
of
each
annual
premium
except
the
first
Claim
300
paid
at
the
time
of
clam
(either
on
death
or
maturity)
0
The
follows
tab.
alculations
should
be
carried
out
using
the
prepared
table
on the
2%
int
(2)
Inthe
column
‘annuity-due
factor’,
calculate
annuity
values
of
the
form:
-
You
can
start
by
entering
the
value
i
5)=0
for
policy
duration
18.
The
value
at
duration
17
can
then
b
cakculated
as
2
function
of
the
duration
18
value.
This
should
lead
t0.3
recursive
formuta
which
you
should
be
able
to
copy
back
up
the
column
50,2
o
populate
the
entries
at
all
ags.
(Other
approaches
are
possible.)
(6)
Usea
simitar
recursive
approach
(or
other
suitable
metho)
to
populte
the
Values
in
the
‘endowment
assurance
factor’
tab.
These
factors
should
be
of
the
form:
)
starting
with
the
vlue
& 11
forpocy
duration
16
(6)
Use
these
factors
as
appropriate
o
calculate
the
prospective
gross
premium
reserve
for
this
polcy
at
each
policy
duration
from
0 to
18
incusive
(noting
that
the
reserve
at
duration
18
s
calculated
immediately
before
the
payment
of
the
maturity
benefit
thatis
then
due,
and
the
reserve
at
duration
0
s
calculated
immediately
before
the
premium
and
expense
that
are
due
at
that
time).
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‘company
wnen
caicuiateo
at
te
vanous
aerent
interest
rates
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-
e
Level
term
assurance
Use
the
question
spreadsheet
to
answer
the
following
question.
Use
the
mortaliy
functions
and
the
annuity
factors
given
on
tab
()
where
approprite.
Aterm
assurance
with
an
18-year
term
has
sum
assured
of
100,000,
which
i
payable
immediately
on
death
during
the policy
term.
The
policyholder
i
aged
exactly
37
at
entry.
Level
annual
premiums
of
230
are
payable
at
the
start
of
each
year
The
insurance
company
uses
a
prospective
formula
and
the
following
basis
for
the
calcuiation
of
itsreserves:
Mortalty:
AMS2
Uitimate
Interest:
3%
po
effective
Initial
expenses:
500
Regular
expenses:
25
paid
at
the
start
of
each
year
excluding
the
first
Initial
commission:
1%
of
the
frst
year's
remium
Renewal
commission:
1.5%
of
each
annual
premium
except
the
first
Claim:
400
paid
at
the
time
of
claim
()
The
following
calculations
should
be
carried
out
using
the
prepared
table
on
tab
().
The
column
headed
‘annuity-due
factor
aready
contains
values
of
the
form
B
curent
e}
o]
(3)
I
the
column
‘term
assurance
factor’,
calculate
term
assurance
values
of
the
form:
Acurert
ge}:
Femamngrera]
You can
start
by
entering
the
value
A,
=0
for
polcy
duration
18.
The
formula
to
cakulate
the
value
at
duration
17
should
be
entered.
The
value
at
duration
16
can
then
be
calculated
25
function
of
the
duration
17
value.
This
should
lead
to
a
recursive
formuia
which
you
should
be able
to
copy
back
up
the
columin
s0.2s
to
populate
the
entries
at
alldurations.
(6)
Use
the
factors
as
appropriate
to
calculate the
prospectve
gross
premium
reserve
forths
policy
at
each
policy
duration
from
0
to 18
inclusive
(noting
that
the
reserve
at
duration
Ois
cakculated
immediately
before
the
premium
and
expense
that
are
due
at
that
time).
(©)
Plotagraph
of
the
reservesat
each
policy
duration
calcuated
in
part
(b),
(6)
Describe
and
briefly
explain
the
pattern
of
reserve
values
you
have
calculated.
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[0}
8y
making
duplicate
copies
of
tab
(),
and
amending
them
as
required,
use
your
spreadsheet
to
recalculate
the
reserves
including
the
graphs)
assuming
the
following
altermative
assumptions
(considered
separately):
()
2%poeffective
(6]
The
inta,
regular
and
ciaim
expenses
are
al
increased
by
SO%.
()
Mortality
rates
are
increased
by
50%
at
each
age.
Describe
the
effect
o
the
change
in
assumptions
on the
reserves,
and
comment
on the
sensitivity
of
the
reserves
to
the
different
assumptions
forths
contract.
Hint
for
()
reconstruct
the
ultimate
mortaity
table
using
odjusted
g,
mortalty
rates.
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Decreasing
term
assurance
Use
the
question
spreadsheet
to
answer
the
following
question.
Use
the
mortalty
functions
and
the
annuity
and
assurance
factors given
on
tab
()
where
approprate.
A
decreasing
term
assurance
with
a
20-year
term
pays
100,000
immediately
on
death
during
the
firstyear
of
the
policy.
The
sum
assured
then
decreases
by
5,000
each
year
50
that
the
amount
payable
on
death
in
the
20th
year
is
5,000.
The
policyholder
is
aged
exactly
40
at
entry.
Level
‘annual
premiums
of
150
are
payable
at
the
start
of
each
year
throughout
the
term.
The
Insurance
company
uses
a
prospective
formula
and
the
folowing
basis
for
the
calculation
of
its
reserves:
Mortalty
AM92
Ultimate
Interest
3%
po
effective
Initial
expenses:
300
Regular
expenses:
25
paid
at
the
start
of
each
year
excluding
the
first
Inital
commission:
5%
of
the
frst
year's
premium
Renewal
commission:
1.5%
of
each
annual
premium
except
the
first
Claim:
300
paid
at
the
time
of
claim
()
The
following
calculations
should
be
carried
out
using
the
prepared
table on
tab
().
The
column headed
"annuity-due
factor
already
contains
values
of
the
form:
{curen
s}
Fomamng
o]
and
the
column headed
‘level
assurance
factor’
contains
values
of
the
form:
leurrent
age}
[remaning
term]
(3)
I
the
column
‘increasing
assurance
factor’,
calculate
increasing
term
assurance
Values
of
the
form:
Bcuen
e
Temamegrom]
for
policy
duration
20.
The
value
You
canstart
by
entering
the
valve
()}
o
at
duration
19
s
equal
to
&%
1
/e
th
levelterm
assurance
factor.
The
value
at
duration
18
can
then
be
calculated
as
function
ofthe
value
at
duration
19,
and
of
the
level
term
assurance
factor
at
duration
18.
This
should
lead
t0.
recursive
formula
which
you
should
be able
to
copy
back
up the
column
50
35
to
populate
the
entries
at
all
durations.
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[0}
term,
which would
cause
al
cover
under
the
policy
to
be
terminated
)
The
insurance
company
has
decided
to
redesign
the
policy
so
that
the
premiums
are
paid
for
a
maximum
of
15
years
or
unti
earber
death),
(3)
Amend
the
spreadsheet
5o
that
premiums
are
payable
according
to
the
new
product
design
(6
Calculate
the
premium
(to
the
nearest
whole
unit)
that
would
need
to
be
paid
under
the
redesigned
policy
that
gves
the
same
reserve
value
at
outset
as
the
initialdesign.
()
With
the
aid
of
a
graph,
describe
and
briefly
explan
the
revised
pattern
of
reserves
for
the
new
product
design.
(@)
Discuss
briely
the
extent
to
which
the
dffculies
due
to
lapses
have been
resolved
by
redesigning
the
contract
in
this
way.
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Retrospective
reserves
—
endowment
assurance
Use
the
question
spreadsheet
to
answer
the
following
question.
Use
the
mortality
functions
and
the
annuity
factors
given
on
tab
(i)
where
appropriate.
An
endowment
assurance
with
an
18-year
term
has
a
sum
assured
of
50,000,
which
is
payable
at
the
end
of
the
term
or
at
the
end
of
the
year
of
earlier
death.
The
policyholder
is
aged
exactly
37
atentry.
Level
annual
premiums
of
2,250
are
payable
at
the
start
of
each
year.
The
insurance
company
uses
a
retrospective
formula
and
the
following
basis
for
the
calculation
of
ts
reserves:
Mortality.
AM92
Ultimate
Interest
3%
po
effective
Initial
expenses:
500
Regular
expenses:
25
paid
at
the
start
of
each
year
excluding
the
first
Claim:
400
paid
at
the
time
of
claim
(death
or
maturity)
()
The
following
calculations
should
be
carried
out
using
the
prepared
table
on tab
(i)
(3)
Populate
the
column
headed
“Annuity-due
factor
at
outset’
with
values
of
the.
form:
7.
erpies
povey
awraton]|
To
do
this,
start
by
inputting
the
numerical
value
of
&,
7]
in
the
first
row.
The
second
and
subsequent
rows
can
be
obtained
recursively
from
the
value
in
the
previous
row
in
each
case.
(b)
Populate
the
column headed
‘Assurance
factor
at
outset’
with
values
of
the
form:
1
A
'37.fexpied
povey
duration]]
To
do
this,
start
by
calculating
the
value
of
A
-
in
the
frst
row.
‘The
second
and
subsequent
rows
can
be
obtained
recursively
from
the
value
in
the
previous
row
in
each
case.
()
Use these
factors
(or
otherwise)
to
calculate
the
retrospective
reserve
for
this
policy
at
each
expired
policy
duration
from
1
to
18
inclusive.
(The
reserve
at
duration
18
should
exclude
the
cost
of
the
maturity
benefit
due
at
that
point.)
(é)
Calculate
the
profit
that the
company
expects
to
make
at
the
maturity
date,
for
each
maturing
policy,
on
this
basis.
Hence
or
otherwise
explain
the
importance
of
the
retrospective
reserve
at
the
maturity
date
for
the
insurance
company.
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e
23
Mkl
e
ccstins
e
Multiple
life
annuities
Use
the
question
spreadsheet
to
answer
the
following
question.
Use
the
I,
functions
provided.
Calculte
the
following
expected
present
values
(EPV),
which
allrelate
to
2
man
currently
aged
‘eactly
60and
2
woman
currently
aged
exactly
7.
‘Assume
that
the
mortalty
of
the
man
follows
the
PMAS2C20
table,
and
that
of
the
woman
follows
the
PFAS2C20
table.
Assume
interest
of
3%
pa
effective
throughout.
()
Ajoint
whole
of
ife
immediate
annuity
of
15,000
po,
pad
in
arrears,
ceasing
on
the
first
death
()
Alast
survivor
whole
of
life
immediate
annuity
of
15,000
pa
paid
in
arrears,
ceasing
on
the
second
death.
Briefy
explain
the
difference
in
the
answer
obtained
compared
to
part
i)
(i)
Areversionary
annuity,
that
pays
aregular
income
of
15,000
pa
starting
on
the
policy
anniversary
following
the
death
of
the
man,
provided
the
woman
i
alive
at
that
point
and
ceasing
on
the
death
of
the
woman.
(W)
Areversionary
annuity,
that
pays
aregular
income
of
15,000
pa
starting
on the
policy
anniversary
following
the
death
of
the
woman,
provided
the
man
i
alive
at
that
point,
and
ceasing
on
the
death
of
the
man.
Briefly
explain
the
difference
in
the
answer
obtained
compared
to
part
(i)
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e
23
Mkl
e
ccsins
Multiple
life
annuities
with
duration
Use
the
question
spreadsheet
to
answer
the
following
question.
Use
the
1,
functions
provided.
Calculte
the
following
expected
present
values
(EPVS),
which
allrelate
to.a
man
currently
aged
‘eactly
60
and
2
woman
currently
aged
exactly
57,
as
appropriate.
‘Assume
that
the
mortalty
of
the
man
follows
the
PMAS2C20
table,
and
that
of
the
woman
follows
the
PFAS2C20
table.
Assume
interest
of
3%
pa
effective
throughout
0
W
)
)
w
)
Ajoint
life
temporary
annuity
of
15,000
pa
payable
in
arears
for
10
years,or
untithe
first
Geath
of
the
man
and
woman,
f
earfer
Alastsurvivor
temporary
annuity
of
15,000
pa paid
in
arrears
for
10
years,
or
until
the
second
death
of
the
man
and
woman
f
earler.
Areversionary
annuity,
that
pays
aregular
income
of
15,000
pa
starting on
the
policy
anniversary
following
the
death
ofthe
man,
provided
the
woman
i
aive
a
that
point,
and
ceasing
on
the
death
of
the
woman,
with
all
payments
ceasing
on
the
10th
policy
anniversary.
Areversionary
annuity,
that
pays
aregular
income
of
15,000
pa starting on the
policy
anniversary
following
the
death
of
the
man,
provided
the
woman
i
alive
a
that
point,
and
ceasing
on
the
death
of
the
woman,
but
only
i
the
man
dies
withn
the
first
10
years.
Areversionary
annuity,
that
pays
aregular
income
of
15,000
pa
starting
on
the
policy
anniversary
following
the
ceath
of
the
man,
provided
the
woman
i
alive
at
that
point,
and
payable
for
10
years
from
that
point
or until
on
the
death
of
the
woman,
i
earler.
Areversionary
annuity,
that
pays
a
regular
income
of
15,000
pa
tarting
on
the
irst
policy
anniversary
that
occurs
at
east
10
years
afte
the
death
of
the
man,
provided
the
woman
isstl
live
at
that
point,
and
ceasing
on the
death
of
the
woman.
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1323
Mot
e
calctations
[
Joint
life
assurance
Use
the
question
spreadsheet
to
answer
the
following
question.
Use
the
1,
functions
provided
Calculate
the
following,
which
all
relate
to
a
man
currently
aged
exactly
60
and
a
woman
currently
aged
exactly
57.
Assume
that
the
mortality
of
the
man
follows
the
PMA92C20
table,
and
that
of
the
woman
follows
the
PFA92C20
table.
Assume
interest
of
3%
pa
effective
throughout,
()
The
expected
present
value
(EPV)
of
a
joint
whole
of
lfe
assurance
that
pays
75,000
at
the
end
of
the
year
in
which
the
first
death
occurs:
(i)
The
gross
level
annual
premium
that
would
be
payable
for
this
policy,
sing
the
equivalence
principle,
assuming
that
©
premiums
are
payable
for
a
maximum
of
25
years,
or
until
the
policy
terminates,
if
earlier
ial
expenses
are
400
©
renewal
expenses,
allincurred
at
the
start
of
each
year
except
the
first,
are 26
(for
the
whole
of
ife)
plus
2%
of
each
premium
(untilthe
premium
ceases)
©
daim
expenses
are
360,
incurred
at
the
end
of
the
year
in
which
the
benefitis
paid,
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()
under
the
three
alternative
scenarios
listed
below.
The
reserve
at
duration
25
should
be
calculated
immediately
before
the
payment
of
the
maturity
benefit
that
is
then
due.
The
possible
scenarios
are:
(1)
onlythe
male
is
alive
at
the
reserve
date
(2)
onlythe
female
is
alive
at
the
reserve
date
(3)
both
people
are
alive
at
the
reserve
date.
Plot
the
reserves
against
duration
for
the
three
scenarios,
on
the
same
graph.
Briefly
‘explain
the
differences
between
them,
and
use
the
graph
to
show
what
happens
to
the
reserve
when
the
first
death
out
of
the
two
lives
happens,
should
that
occur
during
the
policy
term.
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M1
24
Moty
prote
page1
Endowment
assurance
Eighteen
years
ago,
a
life
insurer
sold
1,000
identical
endowment
assurance
policies
to lives
then
aged
exactly
37.
The
policy
term
has
just
ended.
€ach
policy
had
2
sum
assured
of
£75,000
payable
on
maturity
or
immediately
on
earlier
death.
Reserves
were
calculated
using
AM92
Ultimate
mortality
and
interest
of
3%
pa
effective.
These
are
given
in
the
question
spreadsheet,
along
with
an
extract
from
the
AMO92
life
table
and
the
observed
number
of
deaths
in
each
policy
year.
Calculate
the
mortality
profit
for
each
policy
year
assuming
that
the
effective
annual
rate
of
interest
is
3%.
Cw1s
24
oy
prote
paeet
Pure
endowment
On
1
May
2013,
3
ife
insurer
issued
400
pure
endowment
policies
to
ives
then
aged
exactly
60.
Each
policy
had
3
sum
assured
of
£10,000
and
a
term
of
5
years.
The
annual
premiu
for
each
policy
was
£1,750,
and
this
was
payable
on
each
1
May
while
the
policy
was
in
force.
The insurer
held
reserves
that
were
calculated
on
the
following
basis:
Mortality:
PFA92C20
Interest:
2.5%
pa
effective
Expenses:
nil
The
question
spreadsheet
contains:
+
anexract
from
the
PFAS2C20
mortality
table
«
annuity
factors
of
the
form
G,
5
for
£=0,1,2,3,8,
calclated
using
PFAS2C20
mortality
and
2.5%
pa
interest
«
arecord
of
the
actual
number
of
policyholders
who
died
in
each
policy
year.
()
Calculate
the
reserve
per
policy
in
force
at
the
end
of
each
policy
year.
(i)
Calculate
the
insurer's
mortality
prolfit
in
each
policy
year
for
this
group
of
policies
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CM1825:
Competing
ks
[
Dependent
probabilities
and
multiple
decrement
table
Junior
employees
of
a
company
are
subject
to
two
modes
of
decrement
—
death
and
withdrawal
from
employment
Forces
of
mortalty
and
withdrawal
are
assumed
to
be
constant
over
each
year
of
each
year
of
age
and
are
given
below.
Age,
x
Force
of
mortality
Force
of
withdrawal
2
000028
008
2
000029
012
2
000030
010
25
000031
008
These
forces
are
also
given
in
the
question
spreadsheet
for
this
unit.
()
Calculate
the
values
of
(0q)}
and
(oq)}
for
x=22,23,24,25.
Construct
a
multiple
decrement
table
based
on
these
two decrements.
Use
a
radix
of
100,000.
Calculate
the
probability
that
new
employee
aged
exactly
23
will
withdraw
from
service
before
their
25th
birthday.
The
company
introduces
a
death
in
service benefit
that
pays
a
lump
sum
of
£10,000
immediately
on
the
death
of
an
employee
before
age
26.
(W)
Calculate
the
expected
present
value
of
this
benefit
at
the
time
of
recruitment
of
a
new
employee
aged
exactly
22.
Assume
an
effective
annual
rate
of
interest
of
3.5%.
(V)
Itis
now
believed
that
the
force
of
withdrawal
over
the
year
of
age
22
to
23
has
increased
100.10.
Recalculate
the
expected
present
value
of
the
death
in
service benefit
and
comment
on
your
answer.
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CM1825:
Competing
rsks
paeet
EPV
of
disability
benefit
An
employer
provides
a
cash
benefit
of
3
times
salary
immediately
on
disability
before
retirement.
Normal
retrement
age
s
6.
()
Inanew
sheet
named
'EPV',
calculate
the
expected
present
value
of
this
benefit
for
an
employee
now
aged
exactly
61
whose
salary
has
just
increased
to
£80,000.
Basis:
Independent
rates
of
mortality:
ELTIS(Females)
(to
be
entered
manually
from
the
Tables)
Force
of
disability:
002p0
Interest:
5%
po
effective
Salary
increases:
1.8%
on
each
birthday
(i)
Inanew
sheet
named
‘Revised
EPV',
repeat
the
calculation
assuming
that
the
independent
rates
of
mortality
are
those
from
the
ELT1S(Males)
table.
Comment
on
your
answer.
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€M1825:
Competing
ks
[
Varying
forces
of
decrement
and
reconstructing
a
multiple
decrement
table
The
decrement
table
extract
shown
below
is
based
in
the
historical
experience
of
a
large
pension
scheme
Age.
x
ol
(oa)]
(o,
(aa)
a5
13,600
18
50
162
a6
13370
19
52
120
I3
13179
2
6
8
)
13,020
2
)
50
a9
12,855
2
7n
31
50
12,755
Recent
changes
in
employment
conditions
mean
that
the
underlying
annual
force
of
withdrawal
at
each
age
is
now
90%
of
ts
previous
value.
Construct
a
revised
multiple
decrement
table
assuming
that
there
are
no
changes
to
the
forces
of
mortality
and
il-health
retirement.
Give
your
figures
to
one
decimal
place.
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CM1825:
Competing
ks
[
Dependent
probabilities
when
one
decrement
operates
at
the
end
of
the
year
of
age
Members
of
a
pension
scheme
are
subject
to
three
decrements
-
death,
age
retirement
and
illhealth
retirement.
Age
retirements
are
assumed
to
take
place
on
birthdays
whilst
other
decrements
operate
continuously
over
each
year
of
age
before
exact age
65.
Independent
mortality
rates
are
assumed
to
follow
the
PMA92C20
table
(and
you
should
enter
these
into
your
spreadsheet
manually).
Independent
probabilities
of
ll-health
retirement
are
given
by
g,
=0.01+0.005t
,
for
t=01234
‘The
independent
probabilty
of
age
retirement
s
0.2
at
exact
ages
61, 62,
63
and
64.
.
All
active
members
reaching
age
65
must
take
age
retirement
at
that
point.
()
Calculate
the
values
of
(aq){
,
(0a),
and
(aal,
for
x=60,61...,64
(i)
Calculate
the
probability
that
a
member
currently
aged
exactly
61
willretire
at
exact
age
64.
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Cashflow
projection
Use
the
question
spreadsheet
to
answer
the
following
question.
Use
the
mortalty
functions
provided
A
conventional
without-profit
endowment
assurance
is
o
be
ssued
to
a
e
aged
exactl
50.
The
term
i
10
years
and the
sum
assured
(payable
at
the
end
of
the
term
or
at
the
end
of
year
of
earlie
death)
is
10,000.
Level
premiums
of
1,000
pa
are
payable
at
the
startof
each
year
for
10
years,or
untlearler
death
of
the
policyhoider.
()
Ontab
(i),
for
each
year
of
the policy,
calculate
the
total
in-force
expected
cashfiow
(e
expected
income
minus
expected
outgo)
emerging
at
the
end
of
the
year,
per
policy
in
force
at
the
startof
that
year.
Use
the
following
basis:
o
Monaity
AMS2
select
o
merestrate
3%
po
effective
«
initslcommission:
20%
of
one
annwal
premium
+
Renewal
commision
145
of
each
premium
except
the
first
o
it
expenses:
150
o
Renewal
expenses:
25
paincurred
at
the
start
of
each year
except
the
et
+
Deathcaim
expense:
w0
o
Mawntydamexpense:
200
«
Expenseinfiation
Al
non-commission
expense
amounts
are
quoted
a5
3t
outset;they
ae
assumed
toinflate
a
the
rate
of
2%
po
from
outset
o
the
date
of
payment.
(i)
Multiply
each
in-force
expected
cashfiow
from
part
(]
by
the
probabity
of
the
policy
remaining
inforce
from
outset
to
the
start
of
the
relevant
policy
year,
and
so
caculate
the
expected
cashfiow
emerging
at
the
end
of
each
year
as
at
the
policy
commencement
date.
Display
the
expected
cashflows
from
part
(i)
on
a
suitable
graph.
Describe
and
brefly
explain
the
pattern
of
expected
cashfiows
that
have
occurred.
(W)
Describe
the
main
dificulty
tha
this
pattern
of
cashflows
creates
for
the
insurance
company,
and
suggest
steps
that
the
company
s
likely
to
take
to
address
the
problem.
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Profit
test
Use
the
question
spreadsheet
to
answer
the
following
question.
A
conventional
without-profit
endowment
assurance
s
to
be
issued
to
a
ife
aged
exactly
50.
The
term
s
10
years
and
the
sum
assured
(payable
at
the
end
of
the
term
or at
the
end
of
year
of
carlier
death)
s
10,000.
Level
premiums
of
1,000
pa
are
payable
at
the
start
of
each
year
for
10
‘years,or
until
earler
death
of
the
policyholder.
The
expected
cashflows
per
policy
inforce
at
the
start
of
each
year
are
already
calculated
on
the
“Cashflows'
tab,
using
the
mortality
rates
on
the
‘mortality
rates’
tab.
These
cashfiows
assume
the
following
basis:
o
Mortalty
AM92
Select
o
interestrate:
3%
po
effective
«
initial
commission
20%
of
one
annual
premium
+
Renewal
commission:
21%%
of
each
premium
except
the
frst
o
inital
expenses:
150
©
Renewal
expenses
25
paincurred
at
the
start
of
each
year
except
the
first
+
Death
claim
expense:
00
©
Maturity
clsim
expense:
200
+
Expense
infiation
Al
non-comaission
expense
amounts
are
quoted
3s
at
outset;
they
are
assumed
to
inflate
at
the rate
of
2%
po.
from
outset
to
the
date
of
payment.
‘The
insurance
company
also
assumes
it
will
hold
the
following
reserves
for
this
policy:
buation
|
0
|
1
|
2
|
3
|
a
|
s
|
6
|
7
|
&
|
o
Reserve
|
0
|
1450
3,50
|
4,450
|
5,450
|
6,450
|
7,450
|
8,450
|
9,850
These
are
already
input
in
Column
C
of
tab
(i)
()
Use
the
cashfiows
already
calculated, and
the
reserves
provided,
to
calculate
the profit
vector,
profit
signature,
and
Net
Present
Value (NPV)
for
this
contract,
assuming
a
risk
discount
rate
of
3%
pa.
()
Create
a
graph
showing
the
profit
signature
of
the
policy
on
this
basis.
Briefly
describe
the
pattern
of
the
expected
profits
emerging
and
explain
the
role
of
the
reserves
in
producing
this
pattem.
(if)
Repeat
part
(i)
assuming
the
company
does
not
hold
reserves
for
the
policy.
Compare.
your
answer
with
that
of
part
i)
()
Repeat
part
i),
le
including reserves,
but
assuming
arisk
discount
rate
of
7%
pa.
Briefly
explain
the
result
you
obtain.
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Profit
test
with
surrenders
Use
the
question
spreadsheet
to
answer
the
following
question.
A
conventional
without-profit
endowment
assurance
is
to
be
issued
to
a
life
aged
exactly
50.
The
term
s
10
years and
the
sum
assured
(payable
at
the
end
of
the
term
or at
the
end
of
year
of
earlier
death)
is
10,000.
Level
premiums
of
1,000
pa
are
payable
at
the
start
of
each
year
for
10
years,
or
untilthe
earlier
death
of
the
policyholder.
The
expected
cashfiows
per
policy
in
force
at
the
start
of
each
year
are
calculated
on
the
“Cashflows'
tab,
using
the
mortalty
rates on
the
‘Mortality
rates’
tab.
These
cashflows
assume.
the
following
basis:
o
Mortaity
AM92
Select
o
interestrate
3%
po
effective
«
initial
commission
20%
of
one annual
premium
«
Renewal
commission:
1%
of
each
premium
except
the
frst
«
inital
expenses:
150
«
Renewal
expenses
25
paincurred
at
the
start
of
each
year
except
the
first
«
Death
claim
expense:
00
«
Maturity
iaim
expense:
200
©
Expenseinflation
Al
non-commission
expense
amounts
are
quoted
as at
outset;
they
are
assumed
to
inflate
at
the
rate
of
2%
pa
from
outset
to
the
date
of
payment.
“The
profit
signature
and
net
present
value
of
the
policy
are
calculated
on
the
‘Profit’
tab,
assuming
a
risk
discount
rate
of
7%
pa
and
allowing
for
the
following
reserves:
Duration
|
0
1
2
3
T
s
s
|
7
|
s
|
o
Reserve
|
0
|
1,450
|
2,450
|
3450
|
4450
|
5,450
[
6,450
|
7,450
|
850
[
9,450
The
insurance
company
has
decided
it
will
start
paying
surrender
values
on
this
policy.
The
surrender
value
payable
wilfollow
a
formula
that
depends
on
the
duration
at
the
time
of
surrender,
as
follows:
Duration
1
2
3
.
=5
Formula
oszp
07x5P
08xzP
09<Tp
|
o095xp
where
P
means
the
total
premiums
paid
up
to
the
date
of
surrender.
Surrenders
are
only
allowed
at
the
end
of
each
year,
immediately
prior
to
the
date
of
the
first
unpaid
premium.
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e
12628
prof
g
comentans
comocts
‘Amend
the
spreadsheet
as
necessary
50 as
to
calculate
a
revised
net
present
value
allowing
for
the
introduction
of
tis
surrender
benefit,
assuming
the
following
independent
probabilties
of
surrender
apply.
In
this
table,
the
probability
given
for
duration
¢
is
the
probability
that
a
policy,
which
i
in
force
at
that
time,
surrenders
immediately:
Duration
|
1
2
3
[
a
s
[
6
7
[
]o
propabilty
|
0.25
|
015
|
012
|
010
[
008
|
00s
[
004
|
002
[
0or
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Reserves.
Use
the
question
spreadsheet
to
answer
the
following
question.
A
conventional
without-profit
endowment
assurance
is
o
be
ssued
t0
a
e
aged
exactly
50.
The
termis
10
years
and the
sum
assured
(payable
at
the
end
of
the
term
or
a
the
end
of
the
year
of
earlie
death)
is
10,000.
Level
annual
premiums
are
payable
atthe
startof
each
year
for
10
years,
or until
the
earler
death
of
the
policyholder.
‘Assuming
the
policyholder
pays
a
premium
of
1,000
pa
the
expected
cashfiows
per
policy
in
force
at
the
start
of
each
year
are
calulated
on
tab
(),
using
the
mortaity
rates
on the
‘Mortality
rates”
tab.
These
cashfiows
assume
the
following
basis:
o
Moralty
AMS2
select
o
inerestrate
3%
po
effective
©
initial
commission:
20%
of
one
annual
premium
©
Renewal
commisson:
1%
of
each
premium
except
the
first
o
intal
epenses
150
©
Renewal
expenses:
25
poincurred
atthe
start
of
each
year
except
the
irst
«
Deathclaim
expense
00
©
Maurtycaimeense:
200
©
Expense
nfaton
Allnon-commission
expense
amounts
are
quoted
as
at
outset;they
are
assumed
to
inflate
a
the
rate
of
2%
po
from
outset
to
e
date
of
payment
()
Calculate
the
gross
premium
prospective
reserve
for
the
policy on
the
basis
above,
for
policy
durations
09
incusive
(1)
Calculate
the
gross
annual
premium
for
ths
policy using
the
equivalence
principle
and
the
‘assumptions
lsted
above
(e
such
that the
EPV
of
the
future
outgoless
the
EPV
of
the.
future
premiums,
as
at
policy
outset,
i
zero).
Recalculate
the
prospective
gross
premium
reserves
on
the
same
basis using
this
premium.
(i)
Calculate
the
retrospective
gross
premium
reserve,
using
the
new
premium,
on
the
same
basis.
Explain
biefly
why
these
reserves
are
identical
to
the
prospective
reserves
calculated
i
part
(i),
(W)
Calculate
the
retrospective
reserves
at
each
duration
on
the
basis
of
4%
pa Interest,
with
all
other
assumptions
(including
the
premium
payable)
the
same
as
In
part
(i).
Explain
‘why
the
values
have Increased from
before.
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Term
assurance
Use
the
question
spreadsheet
to
answer
the
following
question.
A
conventional
without
profit
term
assurance
s
o
be
issued
to
2
ife
aged
exactly
50.
The
term
s
10years
and
the
sum
assured
is
100,000,
payable
immediately
on
death.
Level
premiums
are
payable
at
the
startof
each
year
for
10
years,
or
until
the
earler
death
of
the
policyholder.
The
insurance
company
uses the
following
basis
to
calculate
ts
reserves
Reserving
basis
The
reserve
is
assumed
to
be
zero
at
policy
outset.
For
durations
1.9,
the
reserve
s
calculated
usinga
gross
premium
prospective
formula,
using
th
following
assumptions:
o
Monaity
AM92
Select
o
Lapses
None
o
inerestate
2%
po
efective
+
Renewal
commission:
1%
of
each
premium
except
th
frst.
+
Renewalexpenses:
30
paincurred
a
the
stat
of
each
year
exceptthe
irst
«
Deathclaim
expense:
500
«
xpenseinfation:
Allnon
commission
expense
amaunts
are
quoted
as
at
utset;
they
re
assumed
to
nflate
at
the
rate
of
3%
pafrom
outset
to
the
date
of
payment
©
Negatvereserves:
Notpermitied
(ia)
Assuming
an
intil
premium
of
600
pa,
calculate
the
reserves
for
this
poicy
a
the
start
of
Years
2-10
inclusive,
using
the
reserving
basis.
Make
sure
the
premium
i
a
variable
that
You
can
easiy
change
in
your
spreadsheet
You
can do
this
as
follows:
(1)
project
the
expected
cashflows
at
the
end
of
each
policy
year
using
the
reserving
basis
(2)
calculate
the
reserve
at
the
startof
Year
10
by
discounting
the
Year
10
cashfiow
and
mutiplying
by
~1
(3)
calculate
the
reserve
at
the
startof
Year
9
from
the
reserve
in
(2)
and
the
expected
cashilow
for
Year
s
(&)
copy
the
formula
up
the
column
to
populate
the
remaining
reserve
values.
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The
insurance
company
calculates
its
premiums
using
the
following
standard
assumptions:
pricng
basis
o
Morainy:
AM92
Select
©
Lapserates
(quoted
as
at
end
of
each
year
per
polcy
then
inforce)
Year
1.
0%
Year2.
3%
Year
0%
Yewsa9:
0%
ver10:
0
o
ierestrate
3%
pa
effective
©
initsl
commision:
20%
of
one
annual
premivm
©
Renewal
commission:
1%%of
each
premium
except
the
first
o
imlepenses:
500
©
Renewal
expenses:
25
poincurred
at
the
start
of
each
year
except
the
first
©
Deathclaim
expense:
400
+
Expenseinfistion:
Allnon-commission
expense
amounts
are
quoted a
at
outset;
they
are
assumed
to
inflateat
the rate
of
2%
pa
from
outset
to
the
date
of
payment
©
Rskdiscountrate:
7%pa
«
profitcrterion
Net
present
value
of
profitto
equal
SO%
of
the
amount
of
inital
()b)
O
the
some
tab,
calculate
the
net
present
value
of
the
contract
using
the
standard
pricing
assumptions
isted
above.
You
should
include
the
reserves
you
have
calculated
in
()a),
making
sure
that
a
zero
reserve
value
is
assumed
if
the
calculated
reserve
turs
out
o
be
negative.
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(i)
Calculate
the
annual
premium
for
thi
contract
using
the
standard
basis.
You ore
recommended
to
make
sufficien
copies
of
the
current
tab
in
order
to
answer
each
of
the
questions
below.
()
Recalculate
the
premium
using
the
standard
assumptions
except
that
the
mortality
probabities
n
the
reserving
basis
are
doubied.
Briefl
explain
and
comment
on
the
result
obtained.
(M)
Recalculate
the
premium
using
the
standard
assumptions
except
that
the
mortality
probabilties
in
both
the
pricng
basis
and
the
reserving
basis
are
doubled.
Brefly
explain
and
comment
on
the
result
obtained.
)
Recalculate
the
premium
using
the
standard
assumptions
except
that
all
apse
rates.
should
be
set
t0
zero.
Briefly
explain
and
comment
on
the
result
obtained.
(W)
Recalculate
the
premium
using
the
standard
assumptions
except
that
the
interest
rate
in
the
priing
basisis
doubled.
Briefl
explain and
comment
on
the
result
obtained.
()
Suggest
why
doubling
the
profittest
mortalty
probabilties
without
changing
the
eserving
basis
would
be
an
unrealistic
scenaro.
(i)
Briefy
summarise
and
explain
the
relative
sensitiviy
of
the
price
of
this
contract
o
the
mortalty,
interest,
and
apse
rate
assumptions
used
in
the
pricing
basis.
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€126
28
sng
ke
s
e
Unit-linked
endowment
assurance
(no
non-unit
reserves)
Use
the
question
spreadsheet
to
answer
the
following
question.
A
unit-inked
endowment
assurance
is
o
be
issued
to
a
ife
aged
exactly
50,
for
a
term
of
10
years.
O
survival
to
the
maturity
date
the bid
value
of
the
unit
fund
is
payable.
On death
before
the
end
of
the
term,
the
higher
of
the
unit
fund
value
(calculated
as
at
the
end
of
the
policy
year
of
death
after
all
charges
have
been
deducted)
or
10,000s
payable
at
the
end
of
the
policy
year
of
death.
A
premium
of
1,000
s
paid
at
the
start
of
each
year.
90%
of
the
first
and
98%
of
allsubsequent
premiums
are
alocated
to
units.
There
is
a
bid-offer
spread
of
5%
and
a
fund
management
charge
of
0.75%
po,
which
i
deducted
from
the
unit
fund
3t
the
end
of
each
policy
year.
()
Calulate
the
net
present
value
of
this
polcy,
using
the
following
assumptions:
o
Mortaity:
AM2
Select
o
Unitgowthrate:
6%
poeffective
©
Nonunitinterest
rate:
3% po
effective
©
initalcommission:
20
of
one
annual
premium
«
Renewal
commission:
1%
of
each
premium
except
the
frst
o
ntelepenses
150
«
Renewal
expenses:
25
paincurred
atthe
startof
each
year
except
the
ist
«
Death
claim
expense:
100
o
Maturityewense:
75
+
Expenseinfistion:
Allnon-commission
expense
amounts
e quoted
as
at
outset;
they
are
assumed
to
inflate
at
the
rate
of
2%
pa
from
outset
to
the
date
of
payment
Riskdiscountrate.
10%po
(i)
Recalculate
the
net
present
value
assurming
a
unit
growth
rate
of
7%
pa
and
briefly
explain
‘why
the net
present
value
has
increased.
()
Using
the
original
assumptions,
calculate
the
largest
firstyear
allocation
rate that
could
be:
used
on the
polcy
that
would
make
the
net
present
value
no
smalle
than
S0%
of
the
inital
commission.
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U262kt
etng
e
s
et
Unit-linked
endowment
assurance
(non-unit
reserves)
Use
the
question
spreadsheet
to
answer
the
following
question.
A
unitlinked
endowment
assurance
i
to
be
issued
to
a
ife
aged
exactly
50, for
aterm
of 10
years.
On
survival
to
the
maturity
date, the
bid
value
of
the
unit
fund
s
payable.
On
death
before
the
nd
of
the
term,
the
higher
of
the
unit
fund
value
(caculated
as
atthe end
of
the
policy
year
of
death
ater
all
charges
have
been
deducted)
or
10,000
s
paid
at
the
end
of
the policy
year
of
death.
A
premium
of
1,000
s
paid
at
the
start
of
each
polcy
year.
65%
of
the
first
and
99%
of
all
subsequent
premiums
are
allocated
to
units.
There
is
a
bid-offer
spread
of
5%
and
a
fund
management
charge
of
0.25%
po,
which
is
deducted
from
the
unit
fund
at
the
end
of
each
policy
year.
‘The
expected
non-unit
cashflows,
per
policy
in
force
at
the
start
of
each
year,
are
given
on
tab
)
of
the
question
spreadsheet.
The
folowing
assumptions
have
been
used
o
Moraity
AM92
Select
©
Untgownmte
6%
poeffective
«
Nonunitinterest
rate:
3%
pa
effective
o
intal
commission:
20%
of
one
annual
premium
«
Renewal
commission:
1%
of
each
premium
except
the
first
o
invalewenses:
150
+
Renewalexpenses:
25
paincurred
atthestart
of
each
year
except
the
first
«
Death
clim
expense:
100
o
Modyepese
75
+
Expenseinfiation:
Al
non-commission
expense
amounts
are
quoted
as at
utset;
they
are
assumed
to
infiate
at
the
rate
of
2%
pa
from
outset
to
the
date
of
payment.
(Ma)
Explan
why
it
s
necessary
for
the
company
to
hold
non-unit reserves
for
this
policy.
()6)
Aftera
separate
investigation,
the
company
decides
to
hokd
the
following
non-unit
reserves
per
policy
in
force
at
each
duration:
owaton
|
1
|
2
|
3
|
4
|
s
|6
|7
|
8
|9
Reseve
|
0
|
0
|
0
|
0
|
10
|
20
|
30
|
@
|
s
Calculate
the net
present
value
for
the
policy
allowing
fo
these
reserves,
using
3
fisk
discount
rate
of
10%
po.
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€18
2628
et
e
s
et
Unit-linked
endowment
assurance
(with
surrenders
and
non-unit
reserves)
Use
the
question
spreadsheet
to
answer
the
following
question.
Aninsurance
company
i
designing
a
unit-linked
endowment
assurance
product.
s
to
b
issued
102
life
aged
exactly
58,
for
a
term
of
10
years.
Under
the
contract,
premium
of
1,000
s
paid
at
the
startof
each
year.
The
company
i
considering
paying
the
following
benefits
under
this
contract
©
o
survival
to
the
maturiy
date
the
unit
fund
value
is
paid
«
atthe
end
of
the
year
of
Geath
before
the
end
of
the
term,
the
higher
of
the
unit
fund
or
the
current
minimum
sum
assured
i
paid
©
atthe
end
of
the
year
of
surrender
during
the
term,
the
unit
fund
value
is
pad.
Al
unitfund
benefits
are
calculated
as
a
the
end
of
the
policy
year
o
caim
after
al
charges
have
been
deducted.
The
minimum
sum
assured
paid
on
death
i
equal
to
10,000
at
the
start
o
the
policy.
The
amount
Increases
at
the
rate
of
10%
pa
compound
50
that
for
examle,
f
the
polcyholder
dies
In
Year
t
(between
durations
¢
1
and
t
),
the
minimum
sum
assured
s
10,000x1.1'"",
payable
at
duration
¢
The
allocation
rate
i
85%
of
each
premium.
There
is
als0
2
bid-offer
spread
of
$%
and
a
fund
management
charge
of
0.75%
pa,
which
is
deducted
from
the
unit
fund
at
the
end
of
each
policy
year.
The
insurer
sets
up
non-unit
reserves
in
order
to
zeroise
any
negative
expected
non-unit
cashfiows,other
than
those occurring
in
the
first
policy
year.
()
Calculate
the
non-unit
reserves required
atthe
start
of
Years
1-10
for
this
policy,
according
to
the
following
assumptions:
o
Mortalty
o2
select
o
Sumender
Independent
probabiltes
of
surrender
apply
according
to
the
table
below,
which
gives
the
probabiity
that
a
poliy,
whichis
n force
at
duration
¢,
surrenders
immediately:
owaton
|
1
|
2
|
3
|
4
|
s
|6
|
7
|
8
|9
probabity
|
020
|
015
|
010
|
00s
|
0025
|
0025
|
0.025
0025
|
0025
«
Untgowthrate:
3%
poefective
«
Nonunitinterestate:
2%
po
efective
+
initislcommission:
20%
of
one
annual
premium
«
Remewal
commission:
4%
of
each
premium
except
th
first
ital
expenses:
150
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Renewal
expenses:
Death
claim
expense:
Surrender
expense:
Maturity expense:
Expense
inflation:
Negative
reserves:
418
2628
4ot
e
comenton
ot
30
paincurred
at
th
stat
of
each
year
except
the
first
100
per
death
claim
100
per
surrender
100
per
maturity
Al
non-commission
expense
amounts
are
quoted
as
at
outset;
they
are
assumed
to
inflate
at
the
rate
of
3%
pa
from
outset
to
the
date
of
payment
Not
permitted
Calculate
the
net
present
value
of
the
profit
o
this
policy,
assuming
the
company
holds
non-unit
reserves
as
calculated
in
part
(1,
isk
discount
ate
of
10%
pa,
and
the
following.
best
estimate
assumptions:
Mortaty,
surrender
a
Unitgrowth
rate:
Nonunit
interest
rate:
Initial
expenses
Renewal
expenses:
Death
claim
expense:
Surender
expense
Maturity
expense:
Expense
infation:
1
commission
rates
same
as
the
reserving
basis
5%
paeffective
3%
po
efective
150
25
paincurred
at
the
start
of
each
year
except
the
irst
100
per
death
laim
75
per
surrender
75
per
maturity
Al
non-commission
expense
amounts
are
quated
as
at
outset;
they
are
assumed
to
infite
at
the
rate
of
2%
pa
from
outset
to
the
date
of
payment
The
company
i
not
saisied
with
the
current
profitabilty
of
this
contract
and
belleves
that
it
surrender
values
are
more
generous
than
those
found
on
similar
products
sold
by
other
nsurance
comganies.
You
are
toinvestigate
the
effect
of
introducing
the
following
scale
of
surrender
penaties
into
the
policy
design,
expressed
a5
a
percentage
of
the
unit
fund
value
at
the
time
of
surrender
Ouration
1
2
3
4
s
|
60
Surrender
penaty
ax
|
2o
|
1%
|
ex
|
%
|
o
Calculate
the
non-unit
reserves
required
for
the
redesigned
contract
according
o
the
assumptions
i
part
the
change.
and
hence
confirm
that
the
non-unt
reserves
are
not
affected
by
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w
Calculate
the net
present
value
for
the
redesigned
contract
using
the
assumptions
in
part
(i)
Explain
briefl
the
impact
that
the
surrender
penalty
has
on
the
expected
profitabity
of
the
polcy
Explain
whether
you
think
the
difference
in
profitabiity
caused
by
the
surrender
penalties
is
kel
to
be
realstic.
Calculate
the
profit
margin
for
the
contractin
part
().
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- Examine the behavior of EUR/USD exchange rate using chartist analysis by concentrating on downtrend reversals between 01.10.2023 and 30.09.2024arrow_forwardExamine the behavior of EUR/USD exchange rate using chartist analysis by concentrating on moving averages between 01.10.2023 and 30.09.2024arrow_forwardGanado Europe (C). Using facts in the chapter for Ganado Europe, assume the exchange rate on January 2, 2016, in Exhibit 11.5 appreciated from $1.2900/€ to $1.5800/€. Calculate Ganado Europe's translated balance sheet for January 2, 2016, with the new exchange rate using the current rate method as shown in the popup window, a. What is the amount of translation gain or loss? b. Where should it appear in the financial statements? Data table a. What is the amount of translation gain or loss? Enter a positive number for a gain and negative for a loss. (Round to the nearest dollar.) (Click on the following icon in order to copy its contents into a spreadsheet.) EXHIBIT 11.5 Ganado Europe's Translation Loss After Depreciation of the Euro: Current Rate Method Assets Cash In Euros (€) (US$/euro) December 31, 2015 Exchange Rate Translated Accounts (US$) January 2, 2016 Exchange Rate (US$/euro) Translated Accounts (US$) 1,500,000 1.2900 $1,935,000 1.5800 $2,370,000 Accounts receivable Inventory…arrow_forward
- Ganado Europe (D). Using facts in the chapter for Ganado Europe, assume that the exchange rate on January 2, 2016, in Exhibit 11.6 appreciated from $1.1100/€ to $1.6200/€. Calculate Ganado Europe's translated balance sheet for January 2, 2016, with the new exchange rate using the temporal rate method as shown in the popup window, E a. What is the amount of translation gain or loss? b. Where should it appear in the financial statements? ..... a. What is the amount of translation gain or loss? Enter a positive number for a gain and negative for a loss. (Round to the nearest dollar.)arrow_forwardUse the NeoZone Calculations Template and FNSACC414_NeoZone Bank Statement to calculate the amounts to be used in the financial reports for the quarter ended 30 June 2022.arrow_forwardGanado Europe (A). Using facts in the chapter for Ganado Europe, assume the exchange rate on January 2, 2016, in Exhibit 11.5 dropped in value from $1.2800/€ to $0.9700/€. Recalculate Ganado Europe's translated balance sheet for January 2, 2016, with the new exchange rate using the current rate method as shown in the popup window, a. What is the amount of translation gain or loss? b. Where should it appear in the financial statements? ... a. What is the amount of translation gain or loss? Enter a positive number for a gain and negative for a loss. (Round to the nearest dollar.)arrow_forward
- Ganado Europe (A). Using facts in the chapter for Ganado Europe, assume the exchange rate on January 2, 2016, in Exhibit 11.5 dropped in value from $1.1400/€ to $0.8700/€. Recalculate Ganado Europe's translated balance sheet for January 2, 2016, with the new exchange rate using the current rate method as shown in the popup window,. What is the amount of translation gain or loss? a. What is the amount of translation gain or loss? Enter a positive number for a gain and negative for a loss. $ (Round to the nearest dollar.) Where should it appear in the financial statements? The translation gain (loss) for the year is added to the balance in the Cumulative Translation Adjustment (CTA) account.arrow_forwardOn September 30, 2020, Peace Frog International (PFI) (a U.S.-based company) negotiated a two- year, 1,600,000 Chinese yuan loan from a Chinese bank at an interest rate of 4 percent per year. The company makes interest payments annually on September 30 and will repay the principal on September 30, 2022. PFI prepares U.S. dollar financial statements and has a December 31 year- end. Relevant exchange rates are as follows: U.S. Dollar per Chinese Yuan ( CNY) $0.160 Date September 30, 2020 December 31, 2020 September 30, 2021 December 31, 2021 September 30, 2022 0.165 0.180 0.185 0.210 a. Prepare all journal entries related to this foreign currency borrowing. b. Taking the exchange rate effect on the cost of borrowing into consideration, determine the effective interest rate in U.S. dollars on the loan in each of the three years 2020, 2021, and 2022.arrow_forwardFrom the following graph explain how the Dollar-Euro Exchange Rate movementduring the period Nov 23, 2016 - Nov 25, 2021? And identify any risks faced byinvestors investing in stock market?arrow_forward
- Please complete the table and show the calculationsarrow_forwardCompare graphically the exchange rates between the two currencies between the period mid 2007 – mid 2009, and between the period mid 2019 – current. Briefly explain.arrow_forwardYou have been presented with the following selected information from the financial statements of one of Canada's largest dairy producers, Saputo Inc. (in $ millions): Statement of financial position 2021 2020 2019 Accounts receivable $1,217 $1,372 $1,248 Inventory 2,294 2,221 1,681 Total current assets 3,948 4,069 3,134 Total assets 13,123 13,793 9,886 Current liabilities 2,146 2,494 1,932 Total liabilities 6,679 7,234 4,465 Statement of income Sales $14,294 $14,944 $13,502 Cost of goods sold 9,575 10,181 9,179 Interest expense 79 96 67 Income tax expense 218 217 230 Net income 626 583 755arrow_forward
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