Compound Interest — Recover principal from total CI over 2 years: At 5% per annum compounded yearly, a sum earns ₹ 410 as compound interest in 2 years. Find the principal.
Aptitude
Compound Interest
Difficulty: Easy
Choose an option
Answer
Correct Answer: ₹ 4000
Explanation
Introduction / Context:When the total compound interest over a fixed number of years is known, and the annual rate is given, we can express that interest directly in terms of the principal and solve for the principal. For 2 years, the growth factor is (1 + r)^2 and the CI equals P[(1 + r)^2 − 1].
Given Data / Assumptions:
- Annual rate r = 5% = 0.05
- Time t = 2 years with annual compounding
- Total CI over 2 years = ₹ 410
- Principal P unknown
Concept / Approach:CI(2y) = P[(1 + r)^2 − 1] = P(2r + r^2) = P(0.10 + 0.0025) = 0.1025 P. Set 0.1025 P = 410 and solve for P.
Step-by-Step Solution:
Compute factor: (1.05)^2 − 1 = 0.1025.Equation: 0.1025 * P = 410.P = 410 / 0.1025 = 4000.Verification / Alternative check:
Forward check: On ₹ 4000, CI(2y) = 4000 * 0.1025 = ₹ 410 (matches).Why Other Options Are Wrong:
- ₹ 8000, ₹ 21000, ₹ 42000, ₹ 4100 do not satisfy 410 = 0.1025 * P.
Common Pitfalls:
- Treating 5% as 5 (forgetting to convert to 0.05).
- Confusing total amount with interest; here ₹ 410 is interest only.
Final Answer:₹ 4000.