You are hoping to buy a house in the future and recently received an inheritance

Question

You are hoping to buy a house in the future and recently received an inheritance of $20, 000. You intend to use your inheritance as a down payment on your house. a. If you put your inheritance in an account that earns 7 percent interest compounded annually, how many years will if be before your inheritance grows top $34, 000? b. If you let your money grow for 10.5 years at 7 percent, how much will you have? c. How long will it take your money to grow to $34, 000 if you move if you move it into an account that pays 4 percent compounded annually? How long will it take your money to grow to $34, 000 if you move it into an account that pays 13 percent? d. What does at this tell you about the relationship among interest rates, time, and future sums? a. If you put your inheritance in an account that earns 7 percent interest compounded annually, how many years will it be before your inheritance grown to $34, 000? years

Explanation / Answer

a. The answer is 8 years

FV = P ( 1+ r) n or 20,000 x ( 1.07) 8 = $ 34,363.74

b. The answer is $ 40,721.04

FV = 20,000 ( 1.07)10.5 = 20,000 x 1.9672 x 1.035 = $ 40,721.04

c. At interest rate of 4%, it will take 14 years

20,000 x ( 1.04)14 = $ 34,633.53

At interest rate of 13%, it will take 5 years

20,000 x ( 1.13)4 = $ 32,609.47

20,000 ( 1.13)5 = $ 36,848

d. Higher the interest rate, shorter the time required to reach a desired future value, and vice versa.

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