9
advanced-math

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

B

$12,400

C

$14,000

D

$13,000

Correct Answer: A

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.