In aptitude (Simple Interest and Compound Interest), in 3 years at simple interest a principal increases by 15% in total. What is the approximate compound interest (in ₹ lakhs) on ₹15 lakhs for 3 years at the same annual rate, compounded annually?

Introduction / Context:
This question again uses the link between simple interest and compound interest. The total simple interest over a certain time is used to infer the underlying annual rate, and that rate is then applied to compute compound interest on a larger principal. The result is expressed in lakhs, which is common in Indian financial aptitude questions.

Given Data / Assumptions:

• In 3 years under simple interest, a principal increases by 15%.
• This implies total simple interest over 3 years is 15% of the principal.
• The annual rate r is the same when we later use compound interest.
• New principal P = ₹15 lakhs.
• Time for CI t = 3 years, compounded annually.
• We must find the approximate compound interest in lakhs of rupees.

Concept / Approach:
Under simple interest: SI = (P * r * t) / 100. We know that total SI in 3 years is 15% of P, so: (P * r * 3) / 100 = 15 * P / 100. After cancelling P / 100 from both sides, we get 3r = 15, hence r = 5% per annum. For compound interest on ₹15 lakhs for 3 years at 5%: Amount A = P * (1 + r / 100)^3 = 15,00,000 * (1.05)^3. Compound interest CI is A minus P. Finally we convert this rupee value into lakhs and approximate according to the options.

Step-by-Step Solution:
Step 1: From simple interest, write (P * r * 3) / 100 = 15 * P / 100. Step 2: Cancel P / 100 on both sides to get 3r = 15. Step 3: Solve for r: r = 15 / 3 = 5% per annum. Step 4: For CI, use P = ₹15,00,000 and t = 3 years with r = 5%. Step 5: Compute the growth factor: 1 + 5 / 100 = 1.05. Step 6: Calculate 1.05^3 = 1.05 * 1.05 * 1.05 = 1.157625. Step 7: Amount A = 15,00,000 * 1.157625 = 17,36,437.5 rupees. Step 8: Compound interest CI = A - P = 17,36,437.5 - 15,00,000 = 2,36,437.5 rupees. Step 9: Convert to lakhs: 2,36,437.5 rupees ≈ 2.364 lakhs, which is approximately ₹2.36 lakhs.

Verification / Alternative check:
We can check using a simpler mental estimate. Over 3 years, simple interest at 5% would give 15% or 0.15 of the principal. On ₹15 lakhs, that would be ₹2.25 lakhs. Since compound interest is only slightly higher than simple interest for modest rates and short periods, we expect the CI to be a bit more than ₹2.25 lakhs. The calculated value of about ₹2.36 lakhs fits this expectation and matches the closest option available.

Why Other Options Are Wrong:
₹2.87 lakhs and ₹3.38 lakhs: Both are too high and would require a higher rate than 5% or a longer time period to be correct.
₹7.81 lakhs: This is far too high compared to a principal of ₹15 lakhs and is not realistic for 3 years at a modest rate.
₹2.10 lakhs: This is slightly lower than the simple interest benchmark of about ₹2.25 lakhs, so it cannot represent compound interest, which should exceed simple interest for the same rate and period.

Common Pitfalls:
A frequent error is to assume that 15% in 3 years means 15% per year, forgetting that simple interest distributes the total percentage gain evenly over the years. Another pitfall is computing compound interest as 15% of the principal plus small corrections without using the proper exponential form. Always isolate the annual rate carefully from the simple interest information before applying compound interest formulas.

Final Answer:
The approximate compound interest on ₹15 lakhs for 3 years at the same rate, compounded annually, is ₹2.36 lakhs.