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 ?$22,000. 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 it be before your inheritance grows to ?$32,000??

b. If you let your money grow for 10.25 years at 7 percent?, how much will you? have?

c. How long will it take your money to grow to ?$32,000 if you move it into an account that pays 4 percent compounded? annually? How long will it take your money to grow to ?$32,000 if you move it into an account that pays 11 percent??

d. What does all 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 grows to ?$32,000??

______(Round to one decimal? place.)

Explanation / Answer

All these questions are simple applications of time value of money function, which states that: FV = PV * (1 + r)n

a. r = 7%, FV = $32,000, PV = $22,000, n = ?

32000 = 22000 * (1 + 7%)n

1.4545 = (1.07)n

Taking log on both sides,

ln (1.4545) = n ln(1.07)

n = ln(1.4545)/ln(1.07) = 5.53 years

b. r = 7%, n = 10.25 years, PV = $22,000, FV = ?

FV = 22000 * (1 + 7%)10.25

FV = 22000 * 2.001

FV = $44,015.58

c. 2 cases, FV = $32,000, PV = $22,000. n = ? when r = 4% and when r = 11%.

32000 = 22000 * (1 + 4%)n

1.4545 = (1.04)n

ln(1.4545) = n ln(1.04)

n = 9.55 years

32000 = 22000 * (1 + 11%)n

1.4545 = (1.11)n

ln(1.4545) = n ln(1.11)

n = 3.59 years

d. By all the above cases, we can see that future value of an amount is a direct function of interest rate earned and number of years to maturity. Higher the interest rate earned, higher will be the future value of a particular sum. Similarly, longer it is allowed to compound, the future value of sum will be higher.

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