Introduction
Compound Interest (CI) is calculated on the principal plus previously accumulated interest
— making it grow exponentially rather than linearly. SSC frequently pairs CI questions with SI in the same
problem to test the relationship between them.
Basic Formula
| Formula |
|---|
| Amount (A) = P × (1 + R/100)ⁿ |
| CI = A − P |
Where P = Principal, R = Rate per annum (%), n = number of years.
Q. Find the CI on ₹10,000 at 10% per annum for 2 years, compounded annually.
A = 10000 × (1.1)² = 10000 × 1.21 = 12,100
CI = 12,100 − 10,000 = ₹2,100
Adjusting for Compounding Frequency
| Compounding Frequency | Adjustment to Formula |
|---|
| Half-yearly | Rate → R/2, Time → 2n |
| Quarterly | Rate → R/4, Time → 4n |
Q. Find the CI on ₹8,000 at 10% per annum for 1 year, compounded half-yearly.
Adjusted rate = 5%, adjusted time periods = 2
A = 8000 × (1.05)² = 8000 × 1.1025 = 8,820
CI = 8,820 − 8,000 = ₹820
CI − SI Relationship (2 Years) — Key Shortcut
Flowchart — Difference Between CI and SI for 2 Years
CI − SI (for 2 years) = P × (R/100)²
This works because the only difference between CI and SI over 2 years is the "interest on first-year interest" — a very common SSC shortcut question type.
Q. The difference between CI and SI on a sum for 2 years at 5% per annum is ₹25. Find the sum.
25 = P × (5/100)² = P × (1/400)
P = 25 × 400 = ₹10,000
CI − SI Relationship (3 Years)
| Formula |
|---|
| CI − SI (for 3 years) = P × R² × (300+R) / 100³ |
Using the "Successive % Change" Formula for CI
💡 Key Insight: Compound interest over multiple years is nothing but repeated application of the successive percentage change formula from Chapter 6 — for 2 years at rate R%, net % increase = R + R + R²/100, which directly gives the same result as the CI formula.
Q. Using the successive-change method, find the amount on ₹5,000 at 10% CI for 2 years.
Net % increase over 2 years = 10 + 10 + (10×10)/100 = 20 + 1 = 21%
Amount = 5000 × 1.21 = ₹6,050
✅ Practice Focus: Basic CI formula and compounding-frequency adjustment · CI-SI difference shortcut for 2 years (P×(R/100)²) · Using successive % change as a CI shortcut · Recognising when a question needs half-yearly/quarterly adjustment.