Multiple choice

Mr. Ahuja invested Rs. 'N' in an index fund and earned a simple interest of 20% per annum and invested Rs. (N + 1000) in an Mutual fund and earned a compound interest 20% per annum. The amount received after 2 years from the Mutual fund is Rs. 2000 more than that from the index fund. Find the sum invested in the Mutual fund.

  1. Rs. 15,000

  2. Rs. 14,000

  3. Rs. 13,500

  4. Rs. 18,000

  5. Rs. 12,000
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A Correct answer
Explanation

Simple Interest (SI) on N at 20% for 2 years = 0.4N. Amount = 1.4N. Compound Interest (CI) on (N+1000) at 20% for 2 years = (N+1000) * (1.2^2 - 1) = (N+1000) * 0.44 = 0.44N + 440. Amount = 1.44N + 1440. Difference = (1.44N + 1440) - 1.4N = 0.04N + 1440 = 2000. 0.04N = 560, so N = 14000. The sum in the mutual fund is N + 1000 = 15000.

AI explanation

The amount from the index fund after two years is N * (1 + 0.40), which equals 1.4N. The amount from the Mutual fund is (N + 1000) * (1.20) squared, which equals 1.44N + 1440. Setting up the equation based on the given difference, 1.44N + 1440 = 1.4N + 2000. Solving this gives 0.04N = 560, so N is 14000, and adding 1000 gives the Mutual fund investment of Rs. 15,000.

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