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advanced-math

$20,000 is borrowed at 9% annual interest compounded monthly. How much is owed after 5 years if no payments are made?

A

$31,423.48

B

$29,000.00

C

$30,772.48

D

$35,000.00

Correct Answer: A

Choice A is the correct answer. Apply monthly compounding to the loan.

  1. Values: P=20000P = 20000, r=0.09r = 0.09, n=12n = 12, t=5t = 5.
  2. Formula: A=20000(1+0.0912)60=20000(1.0075)60A = 20000(1 + \frac{0.09}{12})^{60} = 20000(1.0075)^{60}.
  3. Calculate: (1.0075)601.57117(1.0075)^{60} \approx 1.57117, so A31,423.48A \approx 31,423.48.

💡 Strategic Tip: Monthly rate = 0.0912=0.0075\frac{0.09}{12} = 0.0075, number of periods = 5×12=605 \times 12 = 60.

Choice B is incorrect because this assumes simple interest. Choice C is incorrect because this uses quarterly compounding. Choice D is incorrect because the calculation is wrong.