Compare SI vs CI — Extra interest earned at 6% over 3 years: A person invests at 6% per annum. The simple interest over 3 years is ₹ 900. If interest were compounded annually at the same rate for 3 years on the same principal, how much more interest would be earned?
Aptitude
Compound Interest
Difficulty: Easy
Choose an option
Answer
Correct Answer: Rs. 55.08
Explanation
Introduction / Context:Simple interest (SI) grows linearly with time, whereas compound interest (CI) includes interest on previously earned interest. The “extra” comes from this compounding effect. With the same rate and time, comparing SI and CI on the same principal cleanly quantifies that extra amount.
Given Data / Assumptions:
- SI over 3 years = ₹ 900 at 6% p.a.
- Thus P * 0.06 * 3 = 900 ⇒ P = 900 / 0.18 = ₹ 5000
- CI rate r = 6% per annum, t = 3 years (annual compounding)
Concept / Approach:Compute CI over 3 years: CI = P[(1 + r)^3 − 1]. The extra interest = CI − SI. Plug P = 5000, r = 0.06, t = 3 to get the numeric difference.
Step-by-Step Solution:
Compute growth factor: (1.06)^3 = 1.191016.CI = 5000 * (1.191016 − 1) = 5000 * 0.191016 = ₹ 955.08.SI = ₹ 900 ⇒ Extra = 955.08 − 900 = ₹ 55.08.Verification / Alternative check:
Direct term-by-term compounding confirms the same result; differences arise from interest on prior interest.Why Other Options Are Wrong:
- ₹ 38.13, ₹ 25.33, ₹ 35.30, ₹ 45.00 do not match the computed extra at 6% over 3 years on ₹ 5000.
Common Pitfalls:
- Using 6 as 6% (0.06) confusion; always convert to decimal.
- Forgetting to subtract SI from CI to isolate the “extra”.
Final Answer:Rs. 55.08.