Multiple choice

If the compound interest on a certain sum of money for 2 years is Rs.2,700 and the simple interest on the same sum for the same period is Rs.2,500, the rate of interest will be

  1. 16 percent

  2. 10 percent

  3. 18 percent

  4. 24 percent
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A Correct answer
Explanation

SI for 2 years = 2500, so SI for 1 year = 1250. CI for 2 years = 2700. The difference is the interest on the first year's interest: 2700 - 2500 = 200. Rate = (200 / 1250) * 100 = 16%.

AI explanation

The difference between compound interest and simple interest for two years is found by squaring the simple interest for one year and dividing by the principal. Since the two-year simple interest is 2500, the one-year simple interest is 1250, and the difference between the two interests is 2700 minus 2500, which equals 200. Using the formula 200 equals 1250 squared divided by P gives a principal of 7812.5, and the rate is calculated as 100 times 1250 divided by 7812.5, which is 16 percent.

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