Multiple choice

Mr. Sharma invested a certain sum of money at an annual rate of r% for t years. After t years, he invested the total amount obtained, including interest, at the same annual rate of interest for another t years. If the compound interest accrued during the second period was 26% more than the simple interest accrued during the first period, and the total interest earned at the end of the second period was Rs. 4,520, determine which of the following is correct.

  1. Original sum = 6,000, rate = 8%, time = 3 years

  2. Original sum = 8,000, rate = 10%, time = 2 years

  3. Original sum = 10,000, rate = 8%, time = 3 years

  4. Original sum = 10,000, rate = 10%, time = 2 years

  5. Original sum = 10,000, rate = 7%, time = 3 years
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D Correct answer
AI explanation

For an original sum of 10,000 at 10% simple interest for 2 years, the first period interest is 10000 times 10 times 2 divided by 100, which equals Rs. 2,000. The total amount after the first period becomes 12,000, and reinvesting it at 10% compound interest for another 2 years yields an interest of 12000 times (1.1 squared minus 1), equaling Rs. 2,520. This second period interest is exactly 26% more than the first period interest (2000 times 1.26 equals 2520), and the total interest is 2520 plus 2000 equals Rs. 4,520.

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