Which of the following represents the profit from the investment of x dollars at n percent compound annual interest for 3 years? A. x(1 + 3n/100) – x B. x(1 + n)³/100 – x C. 3x(1 + n/100)² – x D. x(1 + n/100)³ – x E. x(1 + 3n/100)³ – x

(D) Compound interest is annually added to the principal sum. Therefore we can calculate the profit by deducting the original investment amount from the principal sum that we get in three years.

The principal sum increases by (1 + n/100) times each year. Therefore, in three years it increases by (1 + n/100)³ times. Since the original principal sum is x, then the profit is x(1 + n/100)³ – x. The correct answer is choice (D). ---------- I'm confused by your answer. You are told that the investment increases by n%, which is n/100. If we were told that the investment increases by n, then I can understand choosing D as the answer. But as we are already given n as a % (lets say n = 8%, so .08), why would we need to put it over 100 again, as in answer D?

You are told that the investment increases by n%, which is n/100.

That's exactly what we are told. n% = n/100, not n% = n. If n was 0.08, then n% would be (0.08)% = 0.08 × (1/100) = 0.0008

Plug in a value for n in the wording of the question to feel the difference:

"Which of the following represents the profit from the investment of x dollars at 10 percent compound annual interest for 3 years?"

vs.

"Which of the following represents the profit from the investment of x dollars at 10% percent compound annual interest for 3 years?", which is the same as

"Which of the following represents the profit from the investment of x dollars at 0.1 percent compound annual interest for 3 years?"

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