Question

Assume the total cost of a college education will be $410,000 when your child enters college in 15 years. You presently have $68,000 to invest. Required: What annual rate of interest must you earn on your investment to cover the cost of your child’s college education? (Round your answer as directed, but do not use rounded numbers in intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)

Answer 1

12.72%

Step-by-step explanation:

The relationship between the amount invested today and that of the accumulated value after 15 years is that of a present value($68,000) and future value($410,000 ), hence, using the future value formula below we can determine the annual rate of interest:

FV=PV*(1+r)^n

FV=$410,000

PV=$68,000

r=annual rate of interest =unknown

n=investment time horizon=15 years

$410,000=$68,000*(1+r)^15

$410,000/$68,000=(1+r)^15

$410,000/$68,000 can be rewritten as ($410,000/$68,000)^1

($410,000/$68,000)^1=(1+r)^15

divide the indexes on both sides by 15

($410,000/$68,000)^(1/15)=1+r

r= ($410,000/$68,000)^(1/15)-1

r=12.72%