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advanced-math

An investment of $5,000 earns 6% annual interest compounded annually. What is the value after 3 years?

A

$5,955.08

B

$5,900.00

C

$5,300.00

D

$6,000.00

Correct Answer: A

Choice A is the correct answer. Use the compound interest formula.

  1. Formula: A=P(1+r)tA = P(1 + r)^t where P=5000P = 5000, r=0.06r = 0.06, t=3t = 3.
  2. Calculate: A=5000(1.06)3=5000(1.191016)5955.08A = 5000(1.06)^3 = 5000(1.191016) \approx 5955.08.
  3. Result: After 3 years, the investment is worth $5,955.08.

💡 Strategic Tip: For annual compounding, use A=P(1+r)tA = P(1 + r)^t directly.

Choice B is incorrect because this assumes simple interest, not compound. Choice C is incorrect because this only adds one year of interest. Choice D is incorrect because this assumes 20% total growth, not compound.