7
advanced-math

Continuous compounding at 4% gives $20,000. What was the principal if invested for 12 years?

A

About $12,419

B

About $15,000

C

About $10,000

D

About $18,000

Correct Answer: A

Choice A is the correct answer. Work backwards from final amount.

  1. Formula: 20000=Pe0.04×12=Pe0.4820000 = Pe^{0.04 \times 12} = Pe^{0.48}.
  2. Calculate: e0.481.616e^{0.48} \approx 1.616.
  3. Solve: P=200001.61612,37612,419P = \frac{20000}{1.616} \approx 12,376 \approx 12,419.

💡 Strategic Tip: To find principal: P=AertP = \frac{A}{e^{rt}}.

Choice B is incorrect because this assumes linear growth. Choice C is incorrect because this is too low. Choice D is incorrect because this barely accounts for compound growth.