Question

(Future value)  You are hoping to buy a house in the future and recently received an inheritance of ​$16,000. 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 9.75 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 5 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?

Answer 1

Present value = Future value/(1+i)^n

i = interest rate per period

n= number of periods

a)

16000 * (1+7%)^n = 32000

=>

n = ln(2)/ln(1.07)

= 10.25 years

b)

Future value = 16000 * (1+7%)^9.75

= 30946.52

c)

at 5% interest rate

16000 * (1+5%)^n = 32000

=>

n = ln(2)/ln(1.05)

= 14.21 years

at 11% interest rate

n = ln(2)/ln(1.11)

= 6.64 years

d)

Future value is directly proportional to interest rate and time

Higher the interest rate or longer the time then higher will be the future sum