Multiple choice

A bank offers an annual interest rate of r% for 3 years. Using annual compounding, the compound interest (CI) is P [ ( 1 + r 100 ) 3 − 1 ] , and the simple interest (SI) is 3 P r 100 . For the same principal P and rate r, by what percentage is CI greater than SI? (1) r = 8 (2) P = $50,000

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
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A Correct answer
Explanation

CI - SI = P * (1 + r/100)^3 - P - 3Pr/100. The percentage difference is (CI - SI)/SI. This expression depends only on r. Statement (1) gives r, so it is sufficient. Statement (2) gives P, which cancels out in the percentage calculation, so it is not sufficient.

AI explanation

The percentage by which compound interest exceeds simple interest is given by the formula 100 times the quantity ((1 plus r divided by 100) cubed minus 1) divided by (3 times r divided by 100) all minus 100. This formula relies solely on the value of the rate r and does not require the principal P. Since statement 1 provides the rate as 8, you can calculate the exact percentage, making statement 1 alone sufficient. Statement 2 provides the principal, which is irrelevant to finding the percentage difference, so statement 2 alone is not sufficient.

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