The gap between CI and SI — Aptitude Question
The gap between CI and SI: What is the difference between compound and simple interest on ₹8,000 at 10% per annum… Answer and worked solution on CodeKairo.
- Topic: Simple & Compound Interest
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
What is the difference between compound and simple interest on ₹8,000 at 10% per annum for 2 years?
Options
- ₹60
- ₹80
- ₹100
- ₹120
Show the answer and the worked solution
Correct answer: B. ₹80
Worked solution
- Difference for 2 years = P(r/100)² = 8,000 × (0.1)² = 8,000 × 0.01 = ₹80.
- Check: SI = 1,600; CI = 8,000 × 1.21 − 8,000 = 1,680. Difference 80. ✓
Answer: ₹80.
The idea
The two-year gap is the interest earned on the first year's interest, namely P(r/100)². For three years it is P(r/100)²(3 + r/100).
Shortcut. The gap is only year two's interest on year one's interest: year one earns ₹800, and 10% of 800 is ₹80.
Common trap. ₹100 is the tempting round figure, but it would need interest-on-interest at 12.5%; at 10% the ₹800 first-year interest earns just ₹80.
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