Multiple choice

Alice has \$1,000 and Bob has \$900. They want to invest these sums in two different funds that offer the same interest rate of 10%. Fund A offers simple interest, while fund B offers compound interest. Quantity A Interest earned by Alice in fund A over a two-year period Quantity B Interest earned by Bob in fund B over a two-year period

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Alice's simple interest = 1000 * 0.10 * 2 = 200. Bob's compound interest = 900 * (1.10^2 - 1) = 900 * (1.21 - 1) = 900 * 0.21 = 189. Since 200 > 189, Quantity A is greater.

AI explanation

Alice earns simple interest on 1000 at 10% for two years, which equals 1000 multiplied by 0.10 multiplied by 2, giving a Quantity A of 200. Bob earns compound interest on 900 at 10% for two years, which equals 900 multiplied by 1.10 squared minus 900, giving an interest of 189 for Quantity B. Because 200 is greater than 189, Quantity A is greater.

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