In this guide
Interest is one of the most "formula-driven" topics in SSC maths. But candidates who only memorise formulas often get stuck when a question twists them — asking for the rate instead of the interest, or giving the difference between compound and simple interest and asking for the principal. The way through is to connect interest to percentages: simple interest is a fixed percentage of the original amount every year; compound interest is successive percentage growth.
Simple interest (SI)
SI = (P × R × T)/100, and amount = P + SI.
Interest is the same every year because it is always calculated on the original principal.
Worked example: Find the SI on ₹12,000 at 8% per year for 3 years.
SI = 12,000 × 8 × 3/100 = ₹2,880.
Worked example: A sum doubles in 8 years at simple interest. Find the rate.
Interest = P in 8 years, so R × 8 = 100 and R = 12.5%.
Compound interest (CI)
Amount = P × (1 + R/100)^T, and CI = amount − P.
Worked example: CI on ₹10,000 at 10% for 2 years.
Amount = 10,000 × 1.1 × 1.1 = 12,100. CI = ₹2,100.
Year-by-year view
At 10%: Year 1 interest = 1,000; Year 2 interest = 1,000 + 10% of 1,000 = 1,100. Total = 2,100. Compound interest is simple interest plus interest on interest.
CI – SI difference
| Period | Difference |
|---|---|
| 2 years | P × (R/100)² |
| 3 years | P × (R/100)² × (3 + R/100) |
Worked example: The difference between CI and SI on a sum for 2 years at 5% is ₹25. Find the sum.
P × (5/100)² = 25 → P × 1/400 = 25 → P = ₹10,000.
Half-yearly and quarterly compounding
- Half-yearly: rate = R/2, time = 2T.
- Quarterly: rate = R/4, time = 4T.
Worked example: ₹8,000 at 10% per year, compounded half-yearly, for 1 year.
Amount = 8,000 × (1.05)² = 8,000 × 1.1025 = ₹8,820.
Different rates in different years
Amount = P × (1 + R₁/100) × (1 + R₂/100) × …
Worked example: ₹5,000 at 10% in the first year and 20% in the second: 5,000 × 1.1 × 1.2 = ₹6,600.
Doubling and multiples under CI
If a sum becomes 2 times in n years at CI, it becomes 4 times in 2n years and 8 times in 3n years.
Worked example: A sum doubles in 5 years at CI. In how many years will it become 8 times? 15 years.
Effective rate
At 10% compounded half-yearly, the effective annual rate = (1.05)² − 1 = 10.25%.
Instalments
For equal annual instalments that repay a loan at CI, the present values of the instalments add up to the loan.
Worked example: A loan of ₹2,100 is to be repaid in two equal annual instalments at 10% CI. Find each instalment.
Let each = x. x/1.1 + x/1.21 = 2,100 → x(1.1 + 1)/1.21 = 2,100 → x × 2.1/1.21 = 2,100 → x = ₹1,210.
Common traps
| Trap | Correct approach |
|---|---|
| Using annual rate for half-yearly compounding | Halve the rate and double the time |
| Forgetting CI is on the amount, not principal | Use multipliers year by year |
| Confusing amount with interest | Subtract principal at the end |
Practice
- Find the SI on ₹7,500 at 6% per year for 4 years.
- At what rate of SI will a sum triple in 20 years?
- Find the CI on ₹15,000 at 20% for 2 years.
- The difference between CI and SI on ₹20,000 for 2 years is ₹200. Find the rate.
- Find the amount on ₹10,000 at 8% per year compounded quarterly for 6 months.
- A sum becomes ₹17,640 in 2 years and ₹18,522 in 3 years at CI. Find the rate.
Answers: 1. ₹1,800. 2. 10%. 3. ₹6,600. 4. 10%. 5. ₹10,404. 6. 5%.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Staff Selection Commission website .
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