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There is a 60% increase in an amount in 6 years at simple interest. What will be the compound interest on Rs. 12,000 after 3 years at the same rate of interest?

Difficulty: Medium

Correct Answer: Rs. 3972

Explanation:


Introduction / Context:
This question first uses simple interest information to determine the annual rate, and then applies that rate to a different principal under compound interest. It tests the ability to move between simple and compound interest while keeping the rate consistent.


Given Data / Assumptions:

  • An unspecified amount increases by 60% in 6 years under simple interest.
  • The same rate of interest is then used under compound interest for a different principal.
  • Principal for the compound interest part is Rs. 12,000.
  • Time for the compound interest part is 3 years.
  • Interest is compounded annually for the second part.


Concept / Approach:

Under simple interest, a 60% increase over 6 years means total simple interest of 60% of the principal for 6 years. From this, we can find the rate of interest per year. We then apply the compound interest formula A = P * (1 + r / 100)^t for the new principal and time and subtract the principal to get the compound interest.


Step-by-Step Solution:

Step 1: Under simple interest, a 60% increase over 6 years implies SI = 60% of principal in 6 years. Step 2: Simple interest per year as a percentage is 60% / 6 = 10% per annum. Step 3: Therefore the rate r = 10% per annum. Step 4: Now consider the new principal P = 12000 and time t = 3 years under compound interest at r = 10% per annum. Step 5: Amount A = 12000 * (1 + 10 / 100)^3 = 12000 * (1.10)^3. Step 6: Compute (1.10)^2 = 1.21 and (1.10)^3 = 1.331. Step 7: Hence A = 12000 * 1.331 = 15972. Step 8: Compound interest CI = A - P = 15972 - 12000 = 3972.


Verification / Alternative check:

A quick check is to compute simple interest on Rs. 12000 at 10% for 3 years, which would be 12000 * 10 * 3 / 100 = 3600. Because compound interest must exceed simple interest for the same rate and period, the answer must be slightly higher than 3600. The value 3972 matches this expectation.


Why Other Options Are Wrong:

Rs. 2972 is too small and even below the corresponding simple interest. Rs. 4972 and Rs. 5972 are too large for 3 years at 10% and do not result from consistent compounding. Only Rs. 3972 is a correct and reasonable compound interest figure at this rate and period.


Common Pitfalls:

Students sometimes mistakenly assume that a 60% increase in 6 years under simple interest indicates a compound rate directly, which is not correct. Another error is to misinterpret the 60% as a yearly rate instead of an accumulated rate over 6 years. Careful reading of the wording about increase in amount is essential.


Final Answer:

The compound interest on Rs. 12,000 after 3 years at the same rate is Rs. 3972.

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