You plan to retire in exactly 20 years. Your goal is to create a fund that will allow you to receive $120,000 at the end of each year for the 25 years between retirement and death (health studies have indicated that most people die 25 years after retirement). You know that you will be able to earn 3% per year during the 25-year retirement period. $120,000 per year for 25 years TODAY RETIREMENT 20 years later EXPECTED DEATH 25 years later a) How large of a lump-sum will you need to have in your retirement fund at retirement to ensure you can receive/access $120,000 retirement annuity for the
You plan to retire in exactly 20 years. Your goal is to create a fund that will allow you to receive $120,000 at the end of each year for the 25 years between retirement and death (health studies have indicated that most people die 25 years after retirement). You know that you will be able to earn 3% per year during the 25-year retirement period. $120,000 per year for 25 years TODAY RETIREMENT 20 years later EXPECTED DEATH 25 years later a) How large of a lump-sum will you need to have in your retirement fund at retirement to ensure you can receive/access $120,000 retirement annuity for the
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
Related questions
Question
Good day. I need assistance with part c.
Answer for A = $2089577.72
Answer for B = $1406225.90
Transcribed Image Text:You plan to retire in exactly 20 years. Your goal is to create a fund that will allow you to
receive $120,000 at the end of each year for the 25 years between retirement and death
(health studies have indicated that most people die 25 years after retirement). You know
that you will be able to earn 3% per year during the 25-year retirement period.
TODAY
$120,000 per year for 25
RETIREMENT
20 years later
years
EXPECTED DEATH
25 years later
a) How large of a lump-sum will you need to have in your retirement fund at
retirement to ensure you can receive/access $120,000 retirement annuity for the
25 years of your
retirement?
b) What single lump-sum amount should you open your retirement account with
today to ensure the lump-sum amount you calculated, in part a,
part a, is in
retirement fund at retirement? Assume you earn 2% per year during the 20
preceding retirement.
your
years
c) Assume you are unable to open a retirement savings fund today with the single
lump-sum calculated in part b. You are however, given an alternative option to
make annual payments for the next twenty years until retirement. What annual
amount should you pay into the retirement fund to ensure you have the lump-
sum calculated in part a available at the end of the twenty years?
![SELECTED TIME VALUE OF MONEY, STOCK & BOND VALUATION (Not Exhaustive)
FV = PV x (1 + r)n
Future Value of Single Lumpsum
FV = PV ×|1+
FV = CF ×
x
FV = (PV)x(en)
FV = CF x
PV
PV =
=
PV =
PV =
FV
(1+r)"
Vo
1+
PV = CF
V
Bo
=
FV
n
r
V
m
CF
e
CF = FV÷
[(1 + r)"
r
n
FV,
m
r
mxn
(1+r)-1]
II
)
x[₁.
IXn
CF
1
PV =
x - (²) × | |- | + / - |× (1 + r)
X
(1+r)"
CF = (PV ×r) ÷
mxn
xr)+[1
+
J
1
(²=1}x (1 + r)
X
1+r)
V
r
[{{1 + x)² =1]}
r
1
(1+r)"
1-
1
(1+r)"
CF₁ CF₂
(1+r)¹ (1+r)²
+
+
CF₁
n
(1+r)"
Int
=
{ [ - ]} + {
x 1
1
(1+r)"
r
Bo = [I x PV Annuity]+[MxPV]
Par Value (M)
(1+r)"
Future Value of Single Lumpsum when interest
applied more than once but NOT continuously
Future Value of Single Lumpsum when interest
applied continuously
Future Value of Ordinary Annuity
Future Value of Annuity Due
Present Value of Single Lumpsum when
annual interest is applied.
Present Value of Single Lumpsum when
interest is applied more than annually
but not continuously
Present Value of Single Lumpsum when
interest is applied continuously
Present Value of Ordinary Annuity
Present Value of an Annuity Due
Present Value of a Perpetuity
Annual Payment required to
obtain a stipulated value in the
future
Annual Instalment on a loan;
Annual payment when lump-sum
paid/received today
Value/Price of a Financial Asset
Price/Value of Bond with Annual
Interest Payments
(PLEASE CONTINUE TO THE NEXT PAGE)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F49be4e0a-6ab6-4539-be9b-fc0fd79164e4%2F0b63df6c-0968-42f9-ad76-8fc6a67d7535%2Femsbn7f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:SELECTED TIME VALUE OF MONEY, STOCK & BOND VALUATION (Not Exhaustive)
FV = PV x (1 + r)n
Future Value of Single Lumpsum
FV = PV ×|1+
FV = CF ×
x
FV = (PV)x(en)
FV = CF x
PV
PV =
=
PV =
PV =
FV
(1+r)"
Vo
1+
PV = CF
V
Bo
=
FV
n
r
V
m
CF
e
CF = FV÷
[(1 + r)"
r
n
FV,
m
r
mxn
(1+r)-1]
II
)
x[₁.
IXn
CF
1
PV =
x - (²) × | |- | + / - |× (1 + r)
X
(1+r)"
CF = (PV ×r) ÷
mxn
xr)+[1
+
J
1
(²=1}x (1 + r)
X
1+r)
V
r
[{{1 + x)² =1]}
r
1
(1+r)"
1-
1
(1+r)"
CF₁ CF₂
(1+r)¹ (1+r)²
+
+
CF₁
n
(1+r)"
Int
=
{ [ - ]} + {
x 1
1
(1+r)"
r
Bo = [I x PV Annuity]+[MxPV]
Par Value (M)
(1+r)"
Future Value of Single Lumpsum when interest
applied more than once but NOT continuously
Future Value of Single Lumpsum when interest
applied continuously
Future Value of Ordinary Annuity
Future Value of Annuity Due
Present Value of Single Lumpsum when
annual interest is applied.
Present Value of Single Lumpsum when
interest is applied more than annually
but not continuously
Present Value of Single Lumpsum when
interest is applied continuously
Present Value of Ordinary Annuity
Present Value of an Annuity Due
Present Value of a Perpetuity
Annual Payment required to
obtain a stipulated value in the
future
Annual Instalment on a loan;
Annual payment when lump-sum
paid/received today
Value/Price of a Financial Asset
Price/Value of Bond with Annual
Interest Payments
(PLEASE CONTINUE TO THE NEXT PAGE)
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