Multiple choice

The compound interest on a sum for $2$ years is Rs. $832$ and the simple interest on the same sum for the same period is Rs. $800$. The difference between the compound and simple interest for $3$ years will be ?

  1. $66.67$
  2. $36$
  3. $98.56$
  4. $60$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

SI for 2 years = 800, so SI for 1 year = 400. CI for 2 years = 832. The difference of 32 is the interest on the first year's interest (400). Rate = 32/400 = 8%. For 3 years, CI - SI = P * r^2 * (3 + r) / 100^2. P = 400 / 0.08 = 5000. Difference = 5000 * (0.08)^2 * (3.08) = 5000 * 0.0064 * 3.08 = 32 * 3.08 = 98.56.

AI explanation

Using the difference for 2 years, 832 - 800 = 32, so the simple interest for one year is 800 / 2 = 400 and the rate is 32 / 400 = 0.08 or 8%. The formula for the difference between compound interest and simple interest for 3 years is (PR squared / 100 squared) times (300 + R) / 100, which gives P times 0.0064 times 1.08. Solving for the principal P, we have P times 0.08 = 400, so P = 5000. The required difference is 5000 times 0.0064 times 1.08 = 98.56.

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