Question

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

​$18,000.

You intend to use your inheritance as a down payment on your house.

a.  If you put your inheritance in an account that earns

9

percent interest compounded​ annually, how many years will it be before your inheritance grows to

​$30,000​?

b.  If you let your money grow for

10

years at

9

percent​,

how much will you​ have?

c.  How long will it take your money to grow to

​$30,000

if you move it into an account that pays

3

percent compounded​ annually? How long will it take your money to grow to

​$30,000

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?

Answer 1

1. Using financial calculator enter

PV=-18000

FV=30000

I/Y= 9

Solve for N as 5.93

It will take 5.93 years

1. Future value= PV*(1+r)^n

= 18000*1.09^10

= 42612.55

1. At 3%

Using financial calculator enter

PV=-18000

FV=30000

I/Y= 3

Solve for N as 17.28167534

It will take 17.28 years

At 12%

Using financial calculator enter

PV=-18000

FV=30000

I/Y= 12

Solve for N as 4.507469776

It will take 4.51 years

1. At higher interest rate, the future sum will increase faster. It will take lesser number of years to accumulate a certain sum of money when the interest rate is higher. At lower rates, it will take more number of years to accumulate a certain sum of money.