9
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Question 9 • LVA - Mathematical Modeling - Spring

Solve the problem. Round to the nearest cent.Great Dish believes that it will need new equipment in 8 years. The equipment will cost $26,000. What lump sum should be invested today at 12%, compounded semiannually, to yield $26,000?

Answer
A
$20,186.02
B
$16,145.82
C
$16,388.00
D
$10,234.80

Explanation

With semiannual compounding, the rate per period is 12% ÷ 2 = 6%, and 8 years contains 8 × 2 = 16 periods. Discount the future cost to today: $26,000 ÷ (1.06)^16 ≈ $10,234.80. Therefore, the lump sum to invest today is $10,234.80, choice d.

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