6
advanced-math

If continuous compounding at rate rr quadruples an investment in 15 years, what is rr?

A

About 9.2%

B

About 6%

C

About 12%

D

About 15%

Correct Answer: A

Choice A is the correct answer. Solve for rr when investment quadruples.

  1. Equation: 4P=Pe15r4P = Pe^{15r}.
  2. Simplify: 4=e15r4 = e^{15r}.
  3. Natural log: ln(4)=15r\ln(4) = 15r.
  4. Solve: r=ln(4)15=1.386150.0924=9.24%r = \frac{\ln(4)}{15} = \frac{1.386}{15} \approx 0.0924 = 9.24\%.

💡 Strategic Tip: For quadrupling: ln(4)=2ln(2)1.386\ln(4) = 2\ln(2) \approx 1.386.

Choice B is incorrect because this rate is too low. Choice C is incorrect because this rate is too high. Choice D is incorrect because this would more than quadruple.