Compound vs Simple Interest – Extra ₹ 10 after 2 years at 5%: At 5% per annum, the amount at compound interest exceeds that at simple interest by ₹ 10 after 2 years. Find the principal.
Aptitude
Compound Interest
Difficulty: Easy
Choose an option
Answer
Correct Answer: ₹ 4000
Explanation
Introduction / Context:The 2-year CI–SI shortcut gives a direct route to the principal when the excess is known.
Given Data / Assumptions:
- CI − SI = ₹ 10
- r = 5% per annum
- t = 2 years
Concept / Approach:CI − SI over 2 years = P * r^2 / 10000. Solve for P.
Step-by-Step Solution:10 = P * 25 / 10000 → P = 10 / 0.0025P = ₹ 4,000
Verification / Alternative check:SI = 4000 * 5% * 2 = 400; CI = 4000[(1.05)^2 − 1] = 400 + 10 = 410; difference = 10.
Why Other Options Are Wrong:₹ 4050/₹ 5000/₹ 5500 yield excesses different from ₹ 10 at 5% for 2 years.
Common Pitfalls:Forgetting the square on r in the 2-year CI–SI formula.
Final Answer:₹ 4000