3
advanced-math

$2,000 is invested at 8% interest compounded quarterly. What is the value after 2 years?

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

A

$2,343.32

B

$2,320.00

C

$2,160.00

D

$2,400.00

Correct Answer: A

Choice A is the correct answer. Use the compound interest formula for quarterly compounding.

  1. Values: P=2000P = 2000, r=0.08r = 0.08, n=4n = 4 (quarterly), t=2t = 2.
  2. Calculate: A=2000(1+0.084)4×2=2000(1.02)8A = 2000(1 + \frac{0.08}{4})^{4 \times 2} = 2000(1.02)^8.
  3. Compute: (1.02)81.17166(1.02)^8 \approx 1.17166, so A2343.32A \approx 2343.32.

💡 Strategic Tip: Quarterly means n=4n=4, so divide rate by 4 and multiply time by 4.

Choice B is incorrect because this assumes annual compounding, not quarterly. Choice C is incorrect because this uses simple interest. Choice D is incorrect because this calculation is incorrect.