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 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 it into an account that pays 3 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 all this tell you about the relationship among interest rates, time, and future sums?

Answer 1

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 34,000?
=log(34000/20000)/log(1+7%)
=7.842726141

b. If you let your money grow for 10.5 years at 7 percent, how much will you have?
=20000*(1+7%)^10.5
=40696.74373

c. How long will it take your money to grow to $34,000 if you move it into an account that pays 3 percent compounded annually?
=log(34000/20000)/log(1+3%)
=17.95161545

How long will it take your money to grow to $34,000 if you move it into an account that pays 13 percent?
=log(34000/20000)/log(1+13%)
=4.341666904

d. What does all this tell you about the relationship among interest rates, time, and future sums?
If interest rate increases future sum increases
If time increases future sum increases
If interest rate increases time required to accumulate future sum decreases