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advanced-math

For continuous compounding, which rate gives the highest return over 10 years?

A: 5% compounded quarterly B: 4.9% compounded continuously

A

Option B (continuous)

B

Option A (quarterly)

C

They are equal

D

Cannot determine

Correct Answer: B

Choice B is the correct answer. Compare the effective annual rates.

  1. Option A: A=P(1+0.054)4×10=P(1.0125)401.6436PA = P(1 + \frac{0.05}{4})^{4 \times 10} = P(1.0125)^{40} \approx 1.6436P.
  2. Option B: A=Pe0.049×10=Pe0.491.6323PA = Pe^{0.049 \times 10} = Pe^{0.49} \approx 1.6323P.
  3. Comparison: 1.6436>1.63231.6436 > 1.6323, so Option A is better.

💡 Strategic Tip: Higher nominal rate doesn't always win—compounding frequency matters.

Choice A is incorrect because 5% quarterly actually beats 4.9% continuous. Choice C is incorrect because the results differ. Choice D is incorrect because we can calculate and compare.