Compound Interest — Interest That Grows on Itself

Learn Compound Interest through a simple snowball analogy, master the amount formula for annual, half-yearly and quarterly compounding, see a worked example, use the CI-minus-SI shortcuts, and test yourself with a quiz for SSC-CGL.

By the PadhoDost Team · 📖 7 min read · Updated 4 August 2026

Part of SSC CGL & Banking prep

🧠 A rolling snowball

Push a small snowball down a hill. As it rolls it picks up snow, gets bigger, and because it is bigger it picks up even more snow next. Compound Interest works the same way: each year's interest is added to your money, and the next year you earn interest on that bigger total too. Interest starts earning interest — that is 'compounding'.

The difference from Simple Interest is exactly this: in SI the interest is always on the original principal, but in CI the interest is added back so the principal keeps growing. That is why savings, loans, and EMIs in real life almost always use compound interest.

The Main Formulas

amount years principal compound simple
Simple interest grows in a straight line; compound interest curves upward as interest earns interest.
Amount A = P x (1 + R/100)^n (compounded yearly, n = number of years)
Compound Interest CI = A - P = P x [ (1 + R/100)^n - 1 ]
CompoundingRate usedNumber of times (power)
Yearly (annual)R/100n = years
Half-yearlyR/200 (half the rate)2 x years
QuarterlyR/400 (quarter the rate)4 x years
ℹ️ When compounding is more frequent, divide the rate and multiply the power to match the number of periods. Example: 10% per annum for 1 year compounded half-yearly means 5% applied twice.

How to solve a CI problem

  1. 1Identify P, R, and the time.
  2. 2Check how often it compounds — yearly, half-yearly, or quarterly.
  3. 3Adjust the rate and the power to match that frequency.
  4. 4Compute the Amount with A = P x (1 + rate)^power.
  5. 5For CI alone, subtract: CI = A - P.

📝 Worked example

Q: Find the Compound Interest on ₹10,000 at 10% per annum for 2 years, compounded annually.

Given: P = ₹10,000, R = 10, n = 2.

A = 10000 x (1 + 10/100)^2 = 10000 x (1.1)^2

(1.1)^2 = 1.21, so A = 10000 x 1.21 = ₹12,100

CI = A - P = 12100 - 10000 = ₹2,100

Compare: Simple Interest would be 10000 x 10 x 2 / 100 = ₹2,000.

CI is ₹100 more than SI — that extra ₹100 is the interest earned on the first year's interest.

The CI minus SI Shortcut

CI - SI for 2 years = P x (R/100)^2
CI - SI for 3 years = P x (R/100)^2 x (3 + R/100)
💡 Check the worked example with the 2-year shortcut: P x (R/100)^2 = 10000 x (10/100)^2 = 10000 x 0.01 = ₹100. It matches exactly. If a problem gives you the 2-year difference, you can instantly find R or P from this formula.

Remember these

  • CI adds each period's interest back, so you earn interest on interest.
  • Amount A = P x (1 + R/100)^n; CI = A - P.
  • Half-yearly: use R/2 and double the power. Quarterly: use R/4 and quadruple it.
  • CI is always greater than SI for the same P, R, and time (beyond 1 year).
  • 2-year gap: CI - SI = P x (R/100)^2.

⚡ Quick check

What is the difference between the Compound Interest and Simple Interest on ₹5,000 for 2 years at 10% per annum?

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