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Delara invests $4,000 in an account that earns 10% interest compounded annually. Over the same 3 years, a flat 10% simple interest per year would instead have been paid on the original $4,000. By how much does the compound interest earned over the 3 years exceed the simple interest over the 3 years?
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Correct answer
B
Compound balance = 4,000 × 1.1³ = 4,000 × 1.331 = $5,324, so compound interest = $5,324 − $4,000 = $1,324. Simple interest = 4,000 × 0.10 × 3 = $1,200. The difference is $1,324 − $1,200 = $124.
Choice D, $1,324, is the compound interest itself: a solver who correctly expands 1.1³ and finds the compound interest can stop there, having answered how much interest was earned rather than how much more than the simple interest. Choice C, $1,200, reports the simple interest instead of the difference. Choice A, $120, comes from truncating 1.331 to 1.33, understating the compound interest. Choice E, $5,324, reports the final balance rather than the interest earned.
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