Question

Al Derover wants to buy a used vehicle in five years. He estimates the cost will be $12,000. If he invests $8,500 now at a rate of 10% compounded semiannually, how much will he have? Will he have enough money to buy the vehicle at the end of five years? (Round your answer to the nearest cent.)

Answer 1

Future value of investment is calculated as:
Principal*(1+Annual interest rate/Number of compounding periods in a year)^(Number of years the amount is invested*Number of compounding periods in a year)
Given that principal amount=$8,500
Annual interest rate=10%
Number of compounding periods in a year=2 (As the interest rate is compounded semiannually)
Number of years the amount is invested=5 years
Substituting the values in the equation, we get:
Future value of investment=$8,500*(1+10%/2)^(5*2)
=$8,500*(1+5%)^(10)
=$8,500*(1.05)^(10)
=$8500*1.628894627
=$13845.60433 or $13846 (Rounded to the nearest cent)
The person will have an amount of $13846 after 5 years

Cost of the used vehicle=$12,000
So, the person will have enough money to buy the vehicle at the end of five years.