Question

Pete Air wants to buy a used Jeep in 6 years. He estimates the Jeep will cost $17,400. Assume Pete invests $12,400 now at 12% interest compounded semiannually.

a. Calculate the maturity value of the investment. (Do not round intermediate calculations. Round your answer to the nearest cent.)
b. Will Pete have enough money to buy his Jeep at the end of 6 years?
a. Yes
b. No

Answer 1

Using the formula for compound interest, the maturity value of Pete's investment is calculated to be $24,950.81, which would be sufficient to buy the Jeep estimated at $17,400 after 6 years. The correct option is b.

Step-by-step explanation:

To calculate the maturity value of the investment that Pete Air is planning to make for the purchase of a used Jeep in 6 years, we use the formula for compound interest:

A = P(1 + r/n)^(nt)

Given:

• P = $12,400
• r = 12% or 0.12
• n = 2 (since the interest is compounded semiannually)
• t = 6 years

Calculating the maturity value:

A = $12,400(1 + 0.12/2)^(2*6)

A = $12,400(1 + 0.06)^(12)

A = $12,400(1.06)^12

A = $12,400*2.012194 = $24,950.81

Since Pete estimates the Jeep will cost $17,400 and the maturity value of his investment will be $24,950.81, he will have enough money to buy the Jeep at the end of 6 years.

The answer to question b is a. Yes.