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 8 percent interest compounded​ annually, how many years will it be before your inheritance grows to ​$35,000​? b.  If you let your money grow for 10 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 3 percent compounded​ annually? How long will it take your money to grow to ​$35,00 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

1. 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?

FV = PV(1 + r)^t

Solving,

t = ln(FV / PV) / ln(1 + r)

t = ln(35000/16000) / ln(1+0.08)

= 0.7827 / 0.0769

= 10.17 Years

ln is Natural Log

2. If you let your money grow for 10 years at 8 percent, how much will you​ have?

FV = PV(1 + r)^t

       = 16000(1+0.08)¹⁰

     = 20000 * 2.1589

     = $34,542.40

3. How long will it take your money to grow to $35,000 if you move it into an account that pays 3 percent compounded​annually?

FV = PV(1 + r)^t

Solving,

t = ln(FV / PV) / ln(1 + r)

t = ln(35000/16000) / ln(1+0.03)

= 0.7827 / 0.0296

= 26.44 Years

How long will it take your money to grow to $35,000 if you move it into an account that pays 13 percent?

FV = PV(1 + r)^t

Solving,

t = ln(FV / PV) / ln(1 + r)

t = ln(35000/16000) / ln(1+0.13)

= 0.7827 / 0.1222

= 6.40 Years

4. What does all this tell you about the relationship among interest​rates, time, and future​ sums?

1. Any fall in the interest rate would lower future value, with an increase in the holding period will increase future value.
2. Reducing the interest rate reduce the future value factor and ultimately the future value.
3. Increasing the holding period increases the future value factor and thus future value.