Multiple choice

The difference between compound interest, compounded half-yearly, and simple interest on a certain sum of money at the rate of 12% per annum for one year is Rs. 36. Find the sum.

  1. Rs. 10,000

  2. Rs. 12,000

  3. Rs. 14,000

  4. Rs. 15,000

  5. None of these
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A Correct answer
Explanation

SI = P*R*T/100 = P*0.12*1 = 0.12P. CI (half-yearly) = P*(1+0.06)^2 - P = P*(1.1236-1) = 0.1236P. Difference = 0.0036P = 36. P = 36/0.0036 = 10000.

AI explanation

Using the formula for the difference between compound interest compounded half-yearly and simple interest for one year, Difference = P * (R / 200) ^ 2. Substituting the given values of a 36 rupee difference and a 12% annual rate gives 36 = P * (12 / 200) ^ 2. Simplifying this yields 36 = P * 0.0036, meaning the principal sum is Rs. 10,000.

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