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If the simple interest on a sum of money at 5% per annum for 3 years is Rs. 1200, what is the compound interest on the same sum for the same period at the same rate of interest?

Difficulty: Easy

Correct Answer: Rs. 1261

Explanation:


Introduction / Context:
This question directly compares simple interest and compound interest for the same principal, rate, and time. We know the simple interest and must first find the principal. Then we use the compound interest formula to find the required interest amount for the same period and rate.


Given Data / Assumptions:

  • Simple interest for 3 years = Rs. 1200.
  • Rate of interest = 5% per annum.
  • Time period = 3 years.
  • Interest is compounded annually for the compound interest calculation.


Concept / Approach:

Simple interest is given by SI = P * r * t / 100, which we use to find the principal P. Once P is known, compound interest is computed using the formula A = P * (1 + r / 100)^t, and CI = A - P. The interest rate and time remain unchanged between the two calculations.


Step-by-Step Solution:

Step 1: Let the principal be P. Simple interest is SI = P * 5 * 3 / 100. Step 2: So SI = 15P / 100 = 0.15P. Step 3: We are given SI = Rs. 1200. Therefore 0.15P = 1200. Step 4: Solve for P: P = 1200 / 0.15 = 8000. Thus the principal is Rs. 8000. Step 5: For compound interest, amount after 3 years is A = P * (1 + 5 / 100)^3 = 8000 * (1.05)^3. Step 6: Compute (1.05)^2 = 1.1025 and multiply by 1.05 again to get (1.05)^3 = 1.157625. Step 7: Hence A = 8000 * 1.157625 = 9261. Step 8: Compound interest CI = A - P = 9261 - 8000 = 1261.


Verification / Alternative check:

Check that the simple interest on Rs. 8000 at 5% for 3 years is 8000 * 5 * 3 / 100 = 1200, which matches the given value. This confirms that the principal is correct and that the subsequent compound interest calculation is based on the correct principal amount.


Why Other Options Are Wrong:

Rs. 1271, Rs. 1281, and Rs. 1291 are close to the correct value and may attract those who make rounding errors or miscalculate (1.05)^3. However, the exact computation gives a compound interest of Rs. 1261, so all other stated options are incorrect.


Common Pitfalls:

One common error is to confuse the simple interest amount with the compound interest and assume they are equal for small rates or periods. Another mistake is to round the value of (1.05)^3 too early, which can shift the answer. It is important to keep enough decimal accuracy or use exact fractional calculations during the intermediate steps.


Final Answer:

The compound interest is Rs. 1261.

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