Introduction / Context:
Once again, this question connects simple interest information over a long period with compound interest over a shorter period using the same annual rate. From the given overall increase at simple interest, we first deduce the rate and then apply it to find the compound interest on a new principal over 2 years.
Given Data / Assumptions:
- Under simple interest, an amount increases by 40% in 8 years.
- We need to find the annual rate r%.
- Principal for compound interest calculation P = Rs 36,000.
- Time for compound interest n = 2 years.
- Interest is compounded annually in the second part.
Concept / Approach:
A 40% increase in 8 years at simple interest means that total simple interest over 8 years is 40% of the principal. Therefore, the annual simple interest rate is r = 40 / 8 = 5%. We then compute compound interest at 5% per year on Rs 36,000 for 2 years using CI = P * [(1 + r/100)^2 - 1].
Step-by-Step Solution:
Step 1: Convert the given increase to an annual simple interest rate:
r = 40 / 8 = 5% per annum.
Step 2: Compute compound interest on Rs 36,000 for 2 years at 5%.
Step 3: Calculate the compound factor:
1 + r/100 = 1 + 5/100 = 1.05.
Step 4: Square the factor:
1.05^2 = 1.1025.
Step 5: Amount after 2 years:
A = 36,000 * 1.1025 = 39,690.
Step 6: Compound interest:
CI = A - P = 39,690 - 36,000 = Rs 3,690.
Verification / Alternative check:
You can verify by computing year-wise: Year 1 interest = 36,000 * 5% = 1,800, amount = 37,800. Year 2 interest = 37,800 * 5% = 1,890, final amount = 39,690. CI = 3,690, consistent with the direct formula.
Why Other Options Are Wrong:
Rs 4,612.5 and Rs 7,687.5 are too high for only 2 years at 5% compound interest.
Rs 6,150 would require a much higher rate or more than 2 years of compounding.
Common Pitfalls:
Some test takers mistakenly use 40% as the annual rate instead of distributing it over 8 years. Others compute the simple interest again for 2 years instead of using the compound interest formula, missing the interest on accumulated interest.
Final Answer:
The compound interest on Rs 36,000 after 2 years at this rate is Rs 3,690.