Question

(Future value) You are hoping to buy a house in the future and recently received an inheritance of $24,000.You intend to use your inheritance as a down payment on your house.

a. If you put your inheritance in an account that earns 8 percent interest compounded annually, how many years will it be before your inheritance grows to $ 35,000? (Round to one decimal​ place.)

b. If you let your money grow for 10.25 years at 8 percent, how much will you have?

c. How long will it take your money to grow to $35,000 if you move it into an account that pays 5 percent compounded annually? How long will it take your money to grow to $35,000 if you move it into an account that pays 12 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 8 percent interest compounded annually, how many years will it be before your inheritance grows to$30,000 ?

Answer 1

a.

FV=35000

24000*(1+8%)^N=35000

1.08^N=(35000/24000)

take natural log on both sides

N=ln((35000/24000))/ln(1.08)

=4.9 years

b.

how much will you have=24000*(1+8%)^10.25=52820.77 or 52820.8

c.

FV=35000

24000*(1+5%)^N=35000

1.05^N=(35000/24000)

take natural log on both sides

N=ln((35000/24000))/ln(1.05)

=7.7 years

FV=35000

24000*(1+12%)^N=35000

1.12^N=(35000/24000)

take natural log on both sides

N=ln((35000/24000))/ln(1.12)

=3.3 years

d.

as we take higher interest rate, it takes less number of year to reach a future sum, so there is positive relationship between interest rates and future sum.

e.

how many years will it be before your inheritance grows to$30,000

=ln((30000/24000))/ln(1.08)

=2.9 years

the above is answer..