8
advanced-math

$10,000 is invested at 5% annual interest compounded monthly for 3 years. What is the approximate final value?

Use: A=P(1+rn)ntA = P(1 + \frac{r}{n})^{nt}

A

$11,614.72

B

$11,500.00

C

$11,576.25

D

$12,000.00

Correct Answer: A

Choice A is the correct answer. Apply monthly compounding.

  1. Values: P=10000P = 10000, r=0.05r = 0.05, n=12n = 12 (monthly), t=3t = 3.
  2. Calculate: A=10000(1+0.0512)12×3=10000(1.004167)36A = 10000(1 + \frac{0.05}{12})^{12 \times 3} = 10000(1.004167)^{36}.
  3. Result: (1.004167)361.161472(1.004167)^{36} \approx 1.161472, so A11,614.72A \approx 11,614.72.

💡 Strategic Tip: Monthly compounding: divide rate by 12, multiply exponent by 12.

Choice B is incorrect because this assumes simple interest. Choice C is incorrect because this uses quarterly compounding. Choice D is incorrect because the calculation is wrong.