Compound interest earns interest on the interest already earned — which is exactly why it always grows faster than simple interest on the same sum.
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Unlike simple interest, compound interest is recalculated on the NEW total every year, not the original principal.
📌 A = P(1 + R/100)ᵀ
A = final amount, P = principal, R = rate per year, T = number of years.
Worked example: P=₹10,000, R=10%, T=2 years → A = 10,000 × 1.1² = ₹12,100.
Compound Interest = Amount − Principal. CI = 12,100 − 10,000 = ₹2,100.
✨ Half-yearly compounding
Rule
halve the rate, double the periods
10% per year, compounded half-yearly → 5% per period, 2 periods per year
Example
P=₹10,000 for 1 year
A = 10,000 × 1.05² = ₹11,025
For exactly 2 years, there is a one-line formula for the difference between compound and simple interest — no need to calculate both fully.
For 2 years: CI − SI = P × (R/100)². For P=₹5000, R=10%: difference = 5000 × (10/100)² = 5000 × 0.01 = ₹50.
This shortcut ONLY works for exactly 2 years. For 3 years or more, you must calculate CI and SI separately and subtract.
Depreciation uses the exact same formula as compound interest, just SUBTRACTING the rate instead of adding it.
🏆 Depreciation formula
| Formula | Example |
|---|---|
| Value = P × (1 − R/100)ᵀ | A machine worth ₹50,000 depreciates 10% a year. |
| After 2 years | 50,000 × 0.9² = ₹40,500 |
Pro tip: a value that depreciates by the SAME percentage each year never reaches exactly zero — it only gets smaller and smaller, since you always take a percentage of a shrinking amount.
12 questions on compound interest, half-yearly compounding and depreciation.
