Assume you received $8,000 today. Calculate the future value in five years of th

Question

Assume you received $8,000 today. Calculate the future value in five years of the $8,000 if your investments pay a. 6 percent compounded annually b. 8 percent compounded annually c. 10 percent compounded annually d. 10 percent compounded semiannually e. 10 percent compounded quarterly Discuss your answer. Specifically, what do your answers to these questions tell you about the relation between future values and interest rates and between future values and the number of compounding periods per year?

Explanation / Answer

a)6 percent compounded annually

future value in five years of the $8,000 = $8,000*(1.06)5

future value in five years of the $8,000 = $ 10705.81

b)8 percent compounded annually

future value in five years of the $8,000 = $8,000*(1.08)5

future value in five years of the $8,000 = $ 11754.63

c)10 percent compounded annually

future value in five years of the $8,000 = $8,000*(1.1)5

future value in five years of the $8,000 = $ 12884.08

d)10 percent compounded semiannually

no of periods=2*5=10 and per period interest=10%/2=5%

future value in five years of the $8,000 = $8,000*(1.05)10

future value in five years of the $8,000 = $ 13031.16

e)10 percent compounded quarterly

no of periods=4*5=20 and per period interest=10%/4=2.5%

future value in five years of the $8,000 = $8,000*(1.025)20

future value in five years of the $8,000 = $ 13108.93

Seeing above values,

The future values increases as the interest rates increases over a period of time.

The future values increases as the number of compounding periods per year increases over a period of time.

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