### 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...