8
advanced-math

$18,000 earns 6.5% compounded quarterly. What is the balance after 8 years?

A

$30,322.24

B

$27,360.00

C

$28,000.00

D

$32,000.00

Correct Answer: A

Choice A is the correct answer. Use quarterly compounding.

  1. Values: P=18000P = 18000, r=0.065r = 0.065, n=4n = 4, t=8t = 8.
  2. Formula: A=18000(1+0.0654)32=18000(1.01625)32A = 18000(1 + \frac{0.065}{4})^{32} = 18000(1.01625)^{32}.
  3. Calculate: (1.01625)321.68457(1.01625)^{32} \approx 1.68457, so A30,322A \approx 30,322.

💡 Strategic Tip: 8 years quarterly = 8×4=328 \times 4 = 32 periods.

Choice B is incorrect because this assumes annual compounding. Choice C is incorrect because the calculation is wrong. Choice D is incorrect because this is too high.