2
advanced-math

$8,000 invested at 4.5% annual interest compounded semi-annually. What is the value after 6 years?

A

$10,453.86

B

$10,160.00

C

$10,200.00

D

$11,000.00

Correct Answer: A

Choice A is the correct answer. Use semi-annual compounding.

  1. Values: P=8000P = 8000, r=0.045r = 0.045, n=2n = 2 (semi-annually), t=6t = 6.
  2. Formula: A=8000(1+0.0452)2×6=8000(1.0225)12A = 8000(1 + \frac{0.045}{2})^{2 \times 6} = 8000(1.0225)^{12}.
  3. Calculate: (1.0225)121.30673(1.0225)^{12} \approx 1.30673, so A10,453.86A \approx 10,453.86.

💡 Strategic Tip: Semi-annual means twice per year, so n=2n = 2.

Choice B is incorrect because this assumes annual compounding. Choice C is incorrect because the calculation doesn't match. Choice D is incorrect because this growth is too high.