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Question 4 • LVA - Mathematical Modeling - Spring

Solve the problem. Round to the nearest cent.Mathew knows that he will need to buy a new car in 4 years. The car will cost $15,000 by then. How much should he invest now at 10%, compounded quarterly, so that he will have enough to buy a new car?

Answer
A
$12,340.54
B
$11,269.72
C
$10,104.37
D
$9313.82

Explanation

Use the present value formula to find how much invested today will grow to $15,000: PV = FV ÷ (1 + r/n)^(nt). Here, PV = 15,000 ÷ (1 + 0.10/4)^(4×4) = 15,000 ÷ 1.025^16 ≈ $10,104.37. Mathew should invest $10,104.37 now, which is choice C.

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