In aptitude (Simple Interest and Compound Interest), in 2 years at simple interest a principal increases by 18% in total. What will be the compound interest (in ₹) on ₹7,000 for 3 years at the same annual rate, compounded annually?

Introduction / Context:
This question links simple interest and compound interest by giving you the total percentage increase over 2 years under simple interest and then asking for the actual rupee compound interest on a different principal and time period. It tests your ability to infer the annual rate from simple interest information and then correctly apply that rate for compound interest calculations.

Given Data / Assumptions:

• Under simple interest, the principal increases by 18% in 2 years.
• This means total simple interest over 2 years is 18% of the principal.
• The underlying annual rate r is the same for simple and compound interest cases.
• New principal for compound interest calculation P = ₹7,000.
• Time for compound interest t = 3 years, compounded annually.
• We must find the compound interest in rupees for these new conditions.

Concept / Approach:
From the given simple interest statement, 18% increase in 2 years means: Total SI in 2 years = 18% of principal = P * 18 / 100. Simple interest for t years is given by: SI = (P * r * t) / 100. Thus, for 2 years: (P * r * 2) / 100 = P * 18 / 100. By comparing coefficients, we get r * 2 = 18, so r = 9% per annum. Then we use compound interest for 3 years on ₹7,000: Amount = P * (1 + r / 100)^t. Compound interest is Amount minus Principal.

Step-by-Step Solution:
Step 1: From simple interest, write (P * r * 2) / 100 = 18 * P / 100. Step 2: Cancel P / 100 from both sides to get 2r = 18. Step 3: Solve for r: r = 18 / 2 = 9% per annum. Step 4: For compound interest on ₹7,000 for 3 years at 9%, use Amount A = P * (1 + 9 / 100)^3. Step 5: Compute the growth factor: 1 + 9 / 100 = 1.09. Step 6: Calculate 1.09^3 = 1.09 * 1.09 * 1.09 ≈ 1.295029. Step 7: Amount A = 7,000 * 1.295029 ≈ 9,065.203. Step 8: Compound interest CI = A - P = 9,065.203 - 7,000 ≈ 2,065.203. Step 9: Rounded to one decimal place, CI ≈ ₹2,065.2.

Verification / Alternative check:
We can approximate the compound interest by using annual interest additions. Year 1 interest: 9% of 7,000 = 630. New amount = 7,630. Year 2 interest: 9% of 7,630 ≈ 686.7, amount ≈ 8,316.7. Year 3 interest: 9% of 8,316.7 ≈ 748.5, amount ≈ 9,065.2. The total interest is about 9,065.2 - 7,000 = 2,065.2, confirming the earlier calculation.

Why Other Options Are Wrong:
₹1,765.2, ₹1,865.2, and ₹1,965.2: These values are all lower than the correct compound interest and correspond to either lower rates or shorter durations.
₹2,165.2: This is higher than the correct CI, which would require a higher effective rate or more years than the given 3 years at 9%.

Common Pitfalls:
One common mistake is to treat the 18% increase over 2 years as an annual rate of 18%, forgetting to divide by 2 for simple interest. Another error is to compute 3 * 9% and apply 27% directly on ₹7,000 as if it were simple interest, which ignores compounding. Always separate the tasks clearly: first infer the annual rate, then apply compound interest formulas carefully, especially when calculators are not allowed and approximations need to be precise.

Final Answer:
The compound interest on ₹7,000 for 3 years at the same rate, compounded annually, is approximately ₹2,065.2.