Question

1. Future Value. what is the future value in six years of $1000 invested in an account with a stated annual interest rate of 9 percent
a. compounded annually?
b. compounded semi annually?
c. compounded monthly?
d. compounded continuously?
e. why does the future value increase as the compounding period shortens?

Q2. present value and break even interest. consider a firm with a contract to sell an asset for $115,000 three years from now. The asset cost $76,000 to produce today. Given a relevant discount rate on this asset of 13 percent per year, will the firm make a profit on this asset? at what rate does the firm just break even?

Answer 1

Calculate the future value if interest is compounded annually as follows:

Future value = Present value *(1+ Interest rate)^number of periods

= $1,000*(1+9%)^6

= $1000*1.67710

=$1677.10

Future value $1677.10

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Semiannually:

Future value = Present value *(1+ Interest rate)^number of periods

= $1,000*(1+(9%/2))^6*2

= $1000*1.69588

= $1695.88

Future value is $1695.88

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Monthly:

Future value = Present value *(1+ Interest rate)^number of periods

= $1,000*(1+(9%/12))^6*12

= $1000*1.71255

= $1712.55

Future value is $1712.55

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Continuously:

Future value = Present value *(1+ Interest rate)^number of periods

= $1,000*(1+(9%/365))^6*365

= $1000*1.71589

= $1715.89

Future value is $1715.89

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As the compounding period is shorten, interest will be calculated on the accrued interest amount. Therefore, the future amount is increased as the compounding period is decreased.

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