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Pete Air wants to buy a used Jeep in 5 years. He estimates the Jeep will cost $15,000. Assume Pete invests $10,000 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 5 years?

Answer :

The maturity value of the investment will be approximately $17,908.48.

Since the maturity value is greater than the cost of the Jeep, Pete will have enough money to buy his Jeep at the end of 5 years.

How to solve for the maturity value

a. To calculate the maturity value of the investment, we can use the formula for compound interest:

[tex]\[A = P \left(1 + \frac{r}{n}\right)^{nt}\][/tex]

Now, plug in the values:

[tex]\[A = 10,000 \left(1 + \frac{0.12}{2}\right)^{2 \cdot 5}\][/tex]

Calculate the expression inside the parentheses first:

[tex]\[1 + \frac{0.12}{2} = 1.06\][/tex]

Now, calculate the exponent:

[tex]\[2 \cdot 5 = 10\][/tex]

Now, plug these values into the formula:

[tex]\[A = 10,000 \cdot (1.06)^{10}\][/tex]

Now, calculate \(A\):

[tex]\[A \approx 10,000 \cdot 1.7908476974\][/tex]

[tex]\[A \approx 17,908.48\][/tex]

So, the maturity value of the investment will be approximately $17,908.48.

b. To determine if Pete will have enough money to buy his Jeep at the end of 5 years, we compare the maturity value of his investment ($17,908.48) to the estimated cost of the Jeep ($15,000).

Since the maturity value is greater than the cost of the Jeep, Pete will have enough money to buy his Jeep at the end of 5 years.

Read more on maturity value here https://brainly.com/question/30672020

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