Master Compound Interest from Zero

Compound Interest means interest is earned on both principal AND previous interest. Example: ₹1000 at 10% for 2 years. Year 1: Interest=₹100, Amount=₹1100. Year 2: Interest=10% of 1100=₹110, Amount=₹1210. CI = 1210-1000 = ₹210. Compare: SI would be only ₹200!

Key Formulas

CI Amount (Annual)

A = P(1 + R/100)^n

P=principal, R=rate%, n=years

Compound Interest

CI = A - P = P[(1 + R/100)^n - 1]

Subtract principal from amount.

Half-yearly compounding

A = P(1 + R/200)^(2n)

Rate halved, time doubled.

Difference CI and SI (2 years)

CI - SI = P(R/100)²

Very quick formula for 2-year questions!

Difference CI and SI (3 years)

CI - SI = P(R/100)²(3 + R/100)

For 3-year difference questions.

⚡ Shortcut Tricks

2-year shortcut: CI = SI + SI²/(4P). Or simply: CI-SI = PR²/10000.

Effective rate for half-yearly: if R% annually, effective = (1+R/200)²-1 per year.

If CI for 2 years = ₹X and for 1 year = ₹Y, then R = (X-2Y)/Y × 100.

Rule of 72: Money doubles in approximately 72/R years at R% CI.

✏️ Solved Examples

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