Multiple choice

What is the maximum duration, in years, for the accumulated interest earnings from Monica's investments to not exceed her initial investment amount? Monica invests one-fourth of her capital at an annual interest rate of 4%, one-sixth at 6%, and the remaining balance at 12%.

  1. 10

  2. 11

  3. 12

  4. Cannot be determined

  5. a
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the total capital be C. The weighted average interest rate is (1/4 * 4%) + (1/6 * 6%) + (7/12 * 12%) = 1% + 1% + 7% = 9% per annum. To not exceed the initial investment, the total interest must be less than or equal to C, so 0.09 * C * t <= C, which simplifies to t <= 1/0.09 = 11.11 years. The maximum integer duration is 11 years.

AI explanation

Assume Monica's total capital is 120 units, making her investments 30 units at 4%, 20 units at 6%, and the remaining 70 units at 12%. The total annual interest earned is (30 * 4)/100 + (20 * 6)/100 + (70 * 12)/100, which equals 10.8 units per year. To find the maximum duration where the total interest does not exceed her initial capital of 120 units, divide 120 by 10.8 to get 11.11 years, meaning the maximum full years is 11.

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