Question

Stephen plans to purchase a car 7 years from now. The car will cost $60,589 at that time. Assume that Stephen can earn 9.03 percent (compounded monthly) on his money. How much should he set aside today for the purchase? Round the answer to two decimal places. Your Answer:

Answer 1

Solutions:

The cost of the car after 7 years is $60589 ( Future value = $60589)

Rate of return given in the question is 9.03% per annum (r = 9.03%)

Using the time value of money equation -

Future Value = Present Value * ( 1 + r ) ^ n

Here, returns are compounded monthly. Therefore r = annual return / 12 = 9.03/12 = 0.7525%

and n (years) is = 7*12 ( returns compounded monthly, n = 7*12)

$60589 = Present Value * ( 1 + 0.007525 ) ^ (7*12)

$60589 = Present Value * 1.877110428

Pressent Value = $32277.80269

Therefore, Stephen needs to keep $32277.80 aside today to purchase car after 7 years.

To check the answer:

Using the time value of money equation -

Future Value = Present Value * ( 1 + r ) ^ n

= 32277.80 * (1+0.007525)^(7*12)

= $60588.99 = $60589 approximately