4

Set 14: Exponential Functions (Intermediate)

Explanation

Answer: A

An investment of $8,000 at 5.25% compounded continuously for 10 years. Approximate value?

Continuous: A=PertA = Pe^{rt}, use e0.5251.69e^{0.525} \approx 1.69

A.

$13,520

✓ Correct
B.

$12,400

C.

$14,000

D.

$13,000

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Use continuous compounding formula. 1. Formula: A=8000e0.0525×10=8000e0.525A = 8000 \cdot e^{0.0525 \times 10} = 8000 \cdot e^{0.525}. 2. Given: e0.5251.69e^{0.525} \approx 1.69. 3. Calculate: A=8000×1.69=13,520A = 8000 \times 1.69 = 13,520. Strategic Tip: Continuous compounding uses erte^{rt} instead of (1+r)t(1 + r)^t. Choice B is incorrect because the multiplier is wrong. Choice C is incorrect because this is too high. Choice D is incorrect because the calculation doesn't match.

Key Steps:

The correct answer is $13,520

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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