Annual Compounding
With annual compounding the interest for each year is added to the principal before the next year’s interest is computed, so the amount after n years is A = P(1+r/100)ⁿ and the compound interest is A − P. The CAT-smart way is never to expand powers — think in multipliers. A rate of 10% means each year you simply multiply by 1.1, so ₹10,000 for 3 years is 10000 × 1.1 × 1.1 × 1.1 = ₹13,310. For two years you can also use the layered view: interest in year 1 is on P alone; in year 2 it is on P plus year-1 interest, so the "extra" piece is just interest earned on the first year’s interest. Common CAT rates collapse to clean fractions — 25% is ×5/4, 12.5% is ×9/8, 20% is ×6/5 — which keeps the arithmetic exact and fast.
✅ Solved examples
✏️ Practice — try these, take hints as needed
📝 Topic test — 8 questions
Auto-graded with full solutions; saved to your dashboard. Use the calculator and formula sheet (top-right) any time.
Formula Reference Sheet
Core compound interest
| Amount (annual compounding) | A = P(1 + r/100)ⁿ |
|---|---|
| Compound interest | CI = A − P = P[(1 + r/100)ⁿ − 1] |
| Half-yearly compounding | A = P(1 + r/200)^(2n) |
| Quarterly compounding | A = P(1 + r/400)^(4n) |
| Depreciation (value falls r%/yr) | A = P(1 − r/100)ⁿ |
CAT power-tools
| CI − SI for 2 years | P(r/100)² |
|---|---|
| CI − SI for 3 years | P(r/100)²·(3 + r/100) |
| SI for n years | SI = P·r·n/100 |
| Population after n years | P₀(1 + r/100)ⁿ (growth) ; P₀(1 − r/100)ⁿ (decline) |
| Equal yearly instalment (n=2) | each = A / [(1+r/100) + (1+r/100)²] |