Multiple choice

A sum amounts to Rs. 7,562 in 4 years and to Rs. 8,469.44 in 5 years, at a certain rate per cent per annum when the interest is compounded yearly. If Rs. 10,000 at the same rate of interest is borrowed for two years, then what will be the compound interest (in Rs.)?

  1. 2,544

  2. 2,764

  3. 1,965

  4. 1,736
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A Correct answer
Explanation

A4 = P(1+r)^4 = 7562. A5 = P(1+r)^5 = 8469.44. (1+r) = 8469.44 / 7562 = 1.12. So r = 12%. P = 7562 / (1.12)^4 = 7562 / 1.5735 = 4805.8. CI for 2 years at 12% on 10000 = 10000 * (1.12^2 - 1) = 10000 * 0.2544 = 2544.

AI explanation

The interest for the fifth year is 8469.44 minus 7562, which equals 907.44. The yearly compound interest rate is (907.44 divided by 7562) multiplied by 100, equaling 12%. Using the compound interest formula for a principal of 10000 at 12% for two years, the total amount is 10000 multiplied by (1.12)^2, which equals 12544. The compound interest is 12544 minus 10000, resulting in 2544.

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