Description
Answer all the questions in the file
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Explanation & Answer
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ST-3 TIME VALUE OF MONEY
Amount
=$1000
Annual interest rate
=8%
Period
=4 years
a) Find principle
𝐴 = 𝑃(1 + 𝑟)𝑛
1000 = 𝑃(1.08)4
1000
𝑃 = (1.08)4
= $735.03
b)
Amount
=$1000
Annual interest rate
=8%
Period
=4 years
Compounding periods/yr= 4
1000 = 𝑃 (1 +
0.08 4∗4
)
4
= $728.45
c)
If my father offered $221.92 quarterly, or give me $750 on January 1, 2015, I would choose
$221.92 because it would earn more interest.
d)
Principal
Amount
Years
Annual interest rate =?
𝐴 = 𝑃(1 + 𝑟)𝑛
1000 = 750(1 + 𝑟)3
=$750
=$1,000
=3
1000
= (1 + 𝑟)3
750
1.3333=(1 + 𝑟)3
3
3
√1.3333= √(1 + 𝑟)3
1.1006 = 1 + 𝑟
R= 1.1006-1
=0.1006
= 10.06%
e)
principal
amount
years
annual interest rate
$200
$1,000
4
?
𝐴 = 𝑃(1 + 𝑟)𝑛
1000 = 200(1 + 𝑟)4
5 = (1 + 𝑟)4
4
√5 = 1 + 𝑟
1.4953= 1+r
R=0.4953
= 49.53%
f)
Father’s offer
Annual interest rate
Amount
Compounding periods per year
𝑟 2𝑛
𝐴 = 𝑃 (1 + 2)
1000 = 𝑝 (1 +
0.08 2∗2.5
)
2
1000 = 1.21665𝑃
P = $821.9271
=$400
= 8%
=$1000
=2
g) EAR= 𝐸𝐹𝐹% = (1 +
𝐼𝑁𝑂𝑀 𝑁
)
𝑁
2
−1
0.08
) −1
2
𝐸𝐹𝐹% = 8.16%
𝐸𝐹𝐹% = (1 +
INOM=Periodic rate * number of periods per year
0.08*2= 16%
5-1 Opportunity cost
Opportunity cost is the rate of interest a person could earn on an alternative investment with a risk
same as the risk of investment in question. It is the value of r in the Time Value of Money equations
which is displayed at the top of a time line amid the 1st and 2nd tick marks. A single number is not used in
all cases as the opportunity cost rate varies depending on the maturity and riskiness of an investment.
5-3 Annual growt...