1. Formula
A = P(1 + R/100)ⁿ; CI = A − P. Half-yearly: R/2 and 2n periods; quarterly: R/4 and 4n.
2. CI − SI shortcuts
| Years | CI − SI |
|---|---|
| 2 | P(R/100)² |
| 3 | P(R/100)²(3 + R/100) |
3. Effective rates (2 years)
| Rate | CI for 2 years |
|---|---|
| 5% | 10.25% |
| 10% | 21% |
| 20% | 44% |
| Rate r | 2r + r²/100 |
4. Other results
- Doubles in n years → becomes 4 times in 2n, 8 times in 3n years.
- Amounts A₁ (year n) and A₂ (year n + 1) → R = (A₂ − A₁)/A₁ × 100.
- Instalments: each instalment's present value added = loan.
5. Solved examples
(ASO 2021) CI − SI for 2 years at 5% = ₹2.50 → P/400 = 2.5 → P = ₹1,000.
(ASO 2015) ₹2,000 becomes ₹2,205 in 2 years → (1 + r)² = 1.1025 → 5%.
₹8,000 at 10% for 3 years: 8000 × 1.331 = 10,648 → CI ₹2,648.
Sum doubles in 5 years at CI → 8 times in 15 years.
Amount ₹4,840 after 2 years and ₹5,324 after 3 years → R = 484/4840 = 10%.
Solved examples by question type
Each type that comes in the ASO paper, worked step by step. Try it yourself first, then read the solution.
Basic level
Example 1. Find the compound interest on ₹10,000 at 10% per annum for 2 years, compounded annually.
(a) ₹12,100 (b) ₹2,150 (c) ₹2,100 (d) ₹2,000
Answer: (c) ₹2,100
Solution: Amount = 10,000 × (110/100)² = 12,100. CI = 2,100.
Example 2. Find the compound interest on ₹10,000 at 5% per annum for 2 years, compounded annually.
(a) ₹11,025 (b) ₹1,075 (c) ₹1,000 (d) ₹1,025
Answer: (d) ₹1,025
Solution: Amount = 10,000 × (105/100)² = 11,025. CI = 1,025.
ASO exam level
Example 3. The difference between compound and simple interest on ₹8,000 for 2 years at 8% per annum is:
(a) ₹640 (b) ₹51.2 (c) ₹102.4 (d) ₹56.2
Answer: (b) ₹51.2
Solution: For 2 years, CI − SI = P(R/100)² = 8,000 × (8/100)² = ₹51.2.
Example 4. The difference between CI and SI on a sum for 2 years at 4% per annum is ₹20. The sum is:
(a) ₹6,250 (b) ₹12,500 (c) ₹500 (d) ₹13,500
Answer: (b) ₹12,500
Solution: P × (4/100)² = 20 → P = ₹12,500.
Example 5. The difference between CI and SI on a sum for 2 years at 10% per annum is ₹16. The sum is:
(a) ₹2,600 (b) ₹160 (c) ₹800 (d) ₹1,600
Answer: (d) ₹1,600
Solution: P × (10/100)² = 16 → P = ₹1,600.
Example 6. At what rate per annum, compounded annually, will ₹2,000 amount to ₹2,205 in 2 years?
(a) 10% (b) 5.12% (c) 5% (d) 6%
Answer: (c) 5%
Solution: (1 + R/100)² = 2,205/2,000 = 1.1 → 1 + R/100 = 1.05 → R = 5%.
Example 7. Find the compound interest on ₹10,000 for 1 year at 10% per annum, compounded half-yearly.
(a) ₹1,000 (b) ₹11,025 (c) ₹1,025 (d) ₹1,045
Answer: (c) ₹1,025
Solution: Half-yearly: rate 5% for 2 periods. Amount = 10,000 × (105/100)² = 11,025. CI = ₹1,025.
Advanced level
Example 8. A sum doubles itself in 3 years at compound interest. In how many years will it become 4 times?
(a) 12 years (b) 6 years (c) 8 years (d) 9 years
Answer: (b) 6 years
Solution: At CI, the sum keeps doubling every 3 years. 4 = 2^2 → 2 × 3 = 6 years. (Different from SI!)
Example 9. A sum doubles itself in 4 years at compound interest. In how many years will it become 4 times?
(a) 10 years (b) 8 years (c) 12 years (d) 16 years
Answer: (b) 8 years
Solution: At CI, the sum keeps doubling every 4 years. 4 = 2^2 → 2 × 4 = 8 years. (Different from SI!)
Example 10. The difference between CI and SI on ₹8,000 for 3 years at 10% per annum is:
(a) ₹80 (b) ₹258 (c) ₹496 (d) ₹248
Answer: (d) ₹248
Solution: For 3 years, CI − SI = P(R/100)²(3 + R/100) = 8,000 × (10/100)² × 3.1 = ₹248.
Example 11. A sum at compound interest amounts to ₹1,936 in 2 years and ₹2129.6 in 3 years. The rate of interest is:
(a) 5% (b) 9.09% (c) 15% (d) 10%
Answer: (d) 10%
Solution: One year's interest on 1,936 = 193.6. R = 193.6/1,936 × 100 = 10%.
Example 12. A sum at compound interest amounts to ₹2,420 in 2 years and ₹2,662 in 3 years. The rate of interest is:
(a) 15% (b) 10% (c) 5% (d) 9.09%
Answer: (b) 10%
Solution: One year's interest on 2,420 = 242. R = 242/2,420 × 100 = 10%.
Topic-wise practice for Compound interest (Quant): Yearly and half-yearly, CI − SI, instalments, growth. Useful for OPSC ASO, OSSC, OSSSC and other Odisha exams.
Question types covered
- CI compounded yearly
- Half-yearly and quarterly compounding
- Difference between CI and SI for 2 and 3 years
- Sum becomes n times at CI
- Equal annual instalments
- Population growth and depreciation
- Different rates for different years