Concept 1
Identify principal, rate, time and amount
Principal P is the starting sum, interest I is the charge or return, and amount A=P+I. Unless stated otherwise, annual rate R is a percentage per year and time T is measured in years.
Unit rule: convert months to years for an annual simple-interest rate; for compound interest, match rate and number of periods to the compounding frequency.
Concept 2
Simple interest uses the original principal
SI=PRT/100 and A=P(1+RT/100). ₹8,000 at 7.5% per year for 2 years earns 8000×7.5×2/100=₹1,200, so amount=₹9,200.
Because equal interest is added each year, simple-interest amount changes linearly with time.
Concept 3
Compound interest updates the base
With annual compounding, A=P(1+R/100)ⁿ and CI=A−P. ₹10,000 at 10% for 2 years becomes 10000×1.1²=₹12,100, so CI=₹2,100.
For different yearly rates r₁,r₂,…, multiply their growth factors: A=P(1+r₁/100)(1+r₂/100)….
Concept 4
Match rate and period
| Compounding | Rate per period | Periods per year |
|---|---|---|
| Annual | R | 1 |
| Half-yearly | R/2 | 2 |
| Quarterly | R/4 | 4 |
At 12% compounded half-yearly for 18 months, use 6% for 3 half-years: A=P(1.06)³.
Concept 5
The extra CI is interest on interest
For 2 years at R%, CI−SI=P(R/100)². On ₹20,000 at 5%, the difference is 20000×0.05²=₹50.
For 3 years, CI−SI=P[3(R/100)²+(R/100)³]. Derive or apply carefully rather than using the two-year shortcut.
Concept 6
Population growth and depreciation use the same factors
Repeated growth: future value=present value×(1+r/100)ⁿ. Repeated depreciation: future value=present value×(1−r/100)ⁿ.
A machine worth ₹50,000 depreciating 10% yearly is worth 50000×0.9²=₹40,500 after two years.
Worked methods
Examples with reasoning
SI on ₹6,000 at 8% for 15 months
T=15/12 years; SI=6000×8×15/(100×12)=₹600.
CI on ₹8,000 at 5% for 2 years
A=8000×1.05²=₹8,820; CI=₹820.
Amount ₹13,310 after 3 years at 10%
P=13310/1.1³=₹10,000.
₹16,000 at 8% half-yearly for one year
Use 4% twice: A=16000×1.04²=₹17,305.60.
Population 40,000 grows 5%, then falls 5%
40000×1.05×0.95=39,900; equal opposite percentages do not cancel.
Exam traps
Errors that distort time or rate
Months as years
Convert 15 months to 15/12 years for an annual SI rate.
Wrong periodic rate
Half-yearly compounding halves the annual rate and doubles periods.
Interest versus amount
CI=A−P; do not report A when the question asks for interest.
Adding annual changes
Compound growth factors multiply because each year has a new base.
Two-year shortcut
CI−SI=P(R/100)² applies specifically to two years at a constant annual rate.
Opposite rates
Equal percentage rise and fall cause a net decrease, not zero change.
Original practice
Check understanding after learning
Original syllabus-aligned questions—not claimed previous-year questions.
Rapid revision
The one-minute sheet
- SI=PRT/100 and A=P+SI.
- Annual CI amount=P(1+R/100)ⁿ.
- Match periodic rate and number of periods.
- Changing rates require multiplication of successive factors.
- For two years, CI−SI=P(R/100)².
- Depreciation uses (1−r/100)ⁿ.
Source ledger
Official foundations
- SSC CGL official syllabus: Mathematical Abilities
- NCERT official mathematics exemplar directory
- NCERT official textbook portal
Explanations, worked examples and practice are original. Official references are credited and not reproduced. Drafted 24 September 2026.
Partnership: capital, time and profit-sharing ratios.