9
advanced-math

$12,000 is invested at 5.5% compounded quarterly. What is the effective annual rate (approximately)?

A

5.61%

B

5.50%

C

6.00%

D

5.75%

Correct Answer: A

Choice A is the correct answer. Calculate the effective annual rate.

  1. Formula: Effective rate = (1+rn)n1(1 + \frac{r}{n})^n - 1 where r=0.055r = 0.055, n=4n = 4.
  2. Calculate: (1+0.0554)41=(1.01375)41(1 + \frac{0.055}{4})^4 - 1 = (1.01375)^4 - 1.
  3. Result: (1.01375)41.05611=0.0561=5.61%(1.01375)^4 \approx 1.0561 - 1 = 0.0561 = 5.61\%.

💡 Strategic Tip: Compounding more frequently than annually gives a higher effective rate.

Choice B is incorrect because this is the nominal rate, not effective. Choice C is incorrect because this is too high. Choice D is incorrect because the calculation doesn't match.