Multiple choice

The simple interest and compound interest on a certain sum for 2 years is INR 1250 and INR 1475, respectively. The rate of interest per annum (compounded annually) in percentage is:

  1. 12

  2. 24

  3. 36

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For 2 years, SI = 2 * (Principal * Rate) = 1250, so PR = 625. CI = P(1+R)^2 - P = 1475. Substituting P = 625/R into the CI formula: (625/R) * (2R + R^2) = 1475. 1250 + 625R = 1475. 625R = 225. This implies R = 0.36 or 36%.

AI explanation

The difference between compound interest and simple interest over two years is calculated as the simple interest on the first year's interest, given by the formula P times R squared divided by 10000. Here, this difference is 1475 minus 1250, which is INR 225. The simple interest for one year is half of the two-year amount, so the first year interest is 1250 divided by 2, which equals INR 625. The rate of interest per annum is therefore 225 divided by 625 multiplied by 100, resulting in 36 percent.

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