Multiple choice

The amounts of simple interest and compound interest that can be earned on a certain sum in two years at the same rate are Rs. 4000 and Rs. 4180, respectively. What is the rate (per annum) of interest?

  1. 18%

  2. 4.5%

  3. 9%

  4. 12%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simple interest for 2 years = 4000, so SI for 1 year = 2000. Compound interest for 2 years = 4180. The difference is the interest on the first year's interest: 4180 - 4000 = 180. Rate = (180 / 2000) * 100 = 9%.

AI explanation

The difference between compound interest and simple interest for two years is calculated as P times R squared divided by 10000. The difference is 4180 minus 4000, which equals Rs. 180. Since the simple interest for two years is Rs. 4000, the interest for one year is Rs. 2000, meaning the principal is 2000 times 100 divided by R. Substituting into the difference formula, 180 equals 2000 times R divided by 100, so R equals 180 divided by 20, which is 9 percent.

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