3
advanced-math

$30,000 is invested at 7.2% annual interest compounded monthly. How much interest is earned in the first year?

A

$2,235.09

B

$2,160.00

C

$2,300.00

D

$2,500.00

Correct Answer: A

Choice A is the correct answer. Calculate the interest earned.

  1. Values: P=30000P = 30000, r=0.072r = 0.072, n=12n = 12, t=1t = 1.
  2. Final Amount: A=30000(1+0.07212)12=30000(1.006)12A = 30000(1 + \frac{0.072}{12})^{12} = 30000(1.006)^{12}.
  3. Calculate: (1.006)121.0745(1.006)^{12} \approx 1.0745, so A32,235A \approx 32,235.
  4. Interest: 32,23530,000=2,23532,235 - 30,000 = 2,235.

💡 Strategic Tip: Interest earned = Final amount - Principal.

Choice B is incorrect because this uses simple interest, not compound. Choice C is incorrect because the calculation is wrong. Choice D is incorrect because this is too high.