Chapter 5
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MyLab Questions
1.
N = 18
I = 12.5
PV = 0
PMT
? CPT =
2,557.31(a)
3,239.26(b)
FV = 150,000
190,000
PY = 1
CY = 1
2.
N = 10
I =? CPT
= 7.55%
PV = 140
PMT = 0
FV = -290
PY = 1
CY = 1
Chapter 5, Problems, Pg. 157.
1, 2, 4, 10-13, 15, 26, 28, 29, 31, 33
Equivalent
n-
Period Effective Rate = (1 +
r
)
n
− 1
Q1
Your bank is offering you an account that will pay 20% interest in total for a two-year
deposit. Determine the equivalent discount rate for a period length of
a.
six months = (1 +20%)^1/4 – 1 = 4.66%
b.
one year = (1 + 20%)^1/2 -1 = 9.55%
$1,000 x 9.55% = 1,095.50
$1,095.50 x 9.55% = $1,200.12
$1,200.12 - $1,000 = $200.12/$1,000 = 20%
c.
one month =
0.76%
Q2. Do the relevant calculations so you can indicate which you prefer: a bank account that pays
5% per year (EAR) for 3 years or
Option 1 – 5% EAR for 3 Year = $1 x (1.05)^3 = $1.15763
a.
an account that pays 2.5% every 6 months for 3 years?
b.
an account that pays 7.5% every 18 months for 3 years?
c.
an account that pays 0.5% per month for 3 years?
a)
EAR = (1 + 2.5%)^6 = $1.1597
Pick $1
N = 6
I = 2.5
PV = -1
PMT = 0
FV = 1.1597
PY
CY
b)
EAR = (1 + 7.5%)^2 = $1.1556
Pick $1
N = 2
I = 7.5
PV = -1
PMT = 0
FV = 1.1556
PY
CY
Option 1 is better
c)
EAR = (1 + 0.005)^36 = $1.196681
Pick $1
N = 36
I = 0.5
PV = -1
PMT = 0
FV = 1.196681
PY
CY
Option c is better
Q4.
Excel Project
You have found three investment choices for a one-year deposit: 10% APR
compounded monthly, 10% APR compounded annually, and 9% APR compounded daily. Compute the
EAR for each investment choice. (Assume that there are 365 days in the year.)
FORMULA for EAR = (1 + APR/m)^m - 1
A) 10% APR = (1 + 10%/12)^12 -1 =
10.47% EAR
B) 10% APR = 10% EAR
C) 9% APR = (1 + .09/365)^365 -1 = 9.416214%
ICONV = NOM (Nominal rate, APR)
9%
= EFF (Effective Rate)
CPT = 9.416214%
= C/Y (Compounds per year)
365
In Casio = Hit Menu, find TVM, hit a, you will see conversion, input nominal rate,
Q10.
Suppose for its deposit accounts Simplii Financial is offering to pay interest at a rate of 0.25% per
month with monthly compounding, but Tangerine is offering to pay interest at a rate of 0.75% per
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quarter with quarterly compounding. (One quarter is equal to three months.) Which financial institution
is offering the higher rate?
Simplii = (1 + 0.25%) ^3 – 1 = 0.75187% (quarterly compound rate)
Simplii = (1 + 0.25%) ^12 – 1 = 3.0416% EAR
Tangerine = (1 + 0.75%) ^4 – 1 = 3.0339% EAR
11.
You make monthly payments on your car loan. It has a quoted APR of 5% (monthly compounding).
What percentage of the outstanding principal do you pay in interest each month?
What is the effective monthly rate?
5%/12 = 0.4166666
12.
Excel Project
Suppose Capital One is advertising a 60-month, 5.99% APR motorcycle loan. If you
need to borrow $8000 to purchase your dream Harley-Davidson, what will your monthly payment be?
Book
N = 60
I = 5.99%/12 = 0.499167
PV = 8,000
PMT = CPT = -154.62
FV = 0
Alternative
N = 60
I = 5.99
PV = 8,000
PMT = CPT = -154.62
FV = 0
PY = 12
CY = 12
Q13.
Suppose your friend tells you that the Bank of Montreal is offering a 30-year mortgage and your
friend has converted the mortgage’s rate to the equivalent EAR of 6.80%. If you plan to borrow
$150,000, what will your monthly payment be?
Book (we want the APR)
N = 30 x 12 = 360
I = (1 + 6.8%)^1/12 -1 = .
549737
PV = 150000
PMT = CPT =-$957.63
FV = 0
Alternative
N = 360
I = ICONV = EFF 6.8, C/Y = 12, NOM or APR =
6.5968
PV = 150000
PMT = CPT = -$957.63
FV = 0
PY = 12
CY = 12
15.
You have just sold your house for $1,000,000 in cash. Your mortgage was originally a 30-year
mortgage with monthly payments and an initial balance of $800,000. The mortgage is currently exactly
18.5 years old, and you have just made a payment. If the interest rate on the mortgage is 7.75% (APR
with semi-annual compounding), how much cash will you have from the sale once you pay off the
mortgage?
N = 30 x 12 = 360
I = 7.75
PV = 800,000
PMT = CPT = $5,663.87
FV = 0
PY = 12
CY = 2
N = 30 x 12 = 360
I = 7.75………..7.75/2 = 3.875%
(1 + 3.875%)^1/6 -1 =
PV = 800,000
PMT = CPT = $5,663.87
FV = 0
PY = 1
CY = 1
We’ve been told that we have been making monthly payments for 18.5….12 x 18.5 = 222 payments.
Therefore we have 360 – 222 = 138 payments remaining.
N = 138
I = 7.75
PV = CPT = $519,382.01
PMT = $5,663.87
FV = 0
PY = 12
CY = 2
Sell for $1 mill - $519,382.01 = $480,618
Q26.
Excel Project
You have credit card debt of $25,000 that has an APR (monthly compounding) of 15%.
Each month you pay a minimum monthly payment only. You are required to pay only the outstanding
interest. You have received an offer in the mail for an otherwise identical credit card with an APR of 12%.
After considering all your alternatives, you decide to switch cards, roll over the outstanding balance on
the old card into the new card, and borrow additional money as well. How much can you borrow today
on the new card without changing the minimum monthly payment you will be required to pay?
$25,000 x 15%/12 = $312.50
Change the rate to 12%
.....
12%/12 = 1%
Therefore, $312.50/1% = $31,250
$31,250 x 12%/12 = $312.50
Q28
Excel Project
In 1974, the interest rate was 7.782% and the rate of inflation was 12.299% in Canada.
What was the real interest rate in 1974? How would the purchasing power of your savings have changed
over the year?
R = (nom – i)/(1 + i) = (0.0782 - .12299)/(1 + .12299) = -4.02297616%
Q29.
If the rate of inflation is 5%, what nominal interest rate is necessary for you to earn a 3% real
interest rate on your investment?
nom = 1.03 x 1.05 -1 = 8.15%
Q33.
You are thinking about investing $5000 in your friend’s landscaping business. Even though you
know the investment is risky and you can’t be sure of the outcome, you expect your investment to be
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worth $5750 next year. You notice that the rate for one-year treasury bills is 1%. However, you feel that
other investments of equal risk to your friend’s landscape business offer a 10% expected return for the
year. What should you do?
$5750/(1.1) = $5227.2
$5000 x 1.1 = $5500.00…invest with your friend
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-260
1
79.7
2
+
91.2
3
62.4
Terminal CF →
Enter CFs into calculator CF register and enter I
O NPV = ?
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58/45467554/aHR0cHM6Ly9mMi5hcHAUZWRtZW50dWOuY29tL2xlYXJuZXItdWkvc2Vjb25kYXJ5L3VzZXItY...
Unit Activity: Mathematical Models and Investments Each question is worth four points.
Space used (includes formatting): 0/ 15000
15px
A
3
G Part.
Part B
Which investment would earn the most money by retirement at age 65?
1. investing $5,000 in stocks at 6% return at age 25
2. investing $10,000 in bonds at 3% interest at age 35
3. Investing $10,000 in stocks at 8% return at age 45
Explain the reasoning behind your answer.
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BIU X² X₂ .15px
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Help me solve this
View an example
4
Go
arrow_forward
How do I enter this in my calculator to solve?
11.
FV
= PV(1+r/m)^mt
%3D
10,000 = $4,476.20(1+r/1)^(1*10)
= 8.37%
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Saving
nit For
core
Part A The X
omments
B3_Mather x
Directions X
com/courseware-delivery//ua/69158/45467532/aHR0cHM6Ly9mMi5hcHAUZWRtZW50dW0uY29tL2xlYXJuZXItdWkvc2Vjb25kYXJ5L3VzZXItY
Unit Activity: Mathematical Models and Consumer Finance 32 33 0
Space used (includes formatting): 0 / 15000
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LearnerPro X
Space used (Includes formatting): 0/ 15000
M
Determine x
G The balan x +
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Most of the time Matt is fairly good at saving money. However, sometimes he finds that he has little money by the end of the
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spending analysis or only budgeting.
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ric Functions
88 MULTIPLE CHOICE
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What is the equation for the following graph?
4
2
0
π
2π
Bπ
Απ
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-2
A
y=-sin()
B
y=sin()
C
y=sin()
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Use the function f(x)=2x-5
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Previous 21♥ Next → Post Test: Mathematical Models and Investments
Type the correct answer in each box. Use numerals instead of words.
An investment worth $50,000 has these expectations of returns:
• 30% chance of ending up worth $40,000
• 50% chance of ending up worth $50,100
• 20% chance of ending up worth $65,000
Determine the expected value and risk.
The expected value of the investment is $
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mancosaconnect.ac.za/mod/quiz/attempt.php?attempt=1638025&cmid=404551&page=
MANCOSA
Classes
Refer to the incomplete grouped frequency below.
Frequency, Cumulative Midpoint, fm
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Frequency m
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