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
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