Multiple choice

The simple interest on a sum of money for $3$ years at $12\%$ per annum is $rs.\ 4500$. what will be the compound interest on that sum at the same rate and for the same period?

  1. $Rs.\ 5061.60$
  2. $Rs.\ 5000$
  3. $Rs.\ 4050.50$
  4. $Rs.\ 5055$
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A Correct answer
Explanation

Simple interest for 3 years at 12% is 36% of the principal. 0.36P = 4500, so P = 12500. Compound interest = P((1 + 0.12)^3 - 1) = 12500 * (1.404928 - 1) = 12500 * 0.404928 = 5061.60.

AI explanation

First, find the principal by rearranging the simple interest formula S.I. = P × R × T / 100 to get P = 4500 × 100 / (12 × 3), yielding a principal of Rs. 12500. Now, apply the compound interest formula A = P × (1 + R/100)^T to find the amount, which is 12500 × (1.12)^3, resulting in an amount of Rs. 17561.60. Subtracting the principal from this amount gives a compound interest of Rs. 5061.60.

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