Compound Interest Cheat Sheet

Compound Interest Cheat Sheet

Quick Revision

Compound interest (CI) is interest charged on the principal and on the interest already added. Each period's interest becomes part of the principal for the next period.

Ready to practise? Take the Simple and Compound Interest quiz

1. The Core Formulas

For principal P, rate r% per year, and n years:

Amount, A = P × (1 + r/100)ⁿ
Compound Interest = A − P

2. Compounding More Than Once a Year

Example (half-yearly)

P = ₹8000, r = 10% per year, time = 1 year, compounded half-yearly:

A = 8000 × (1 + 5/100)² = 8000 × 1.1025 = ₹8820
CI = 8820 − 8000 = ₹820

3. CI vs SI

Simple interest uses the original principal every year: SI = PRT/100. Compound interest grows faster because it earns on the added interest. For the first year (compounded yearly) CI and SI are equal; from the second year CI is larger.

4. Difference Between CI and SI (shortcut)

For the same P, r and time:

2 years:  Difference = P × (r/100)²
3 years:  Difference = P × (r/100)² × (3 + r/100)

Example

P = ₹5000, r = 10%, 2 years:

Difference = 5000 × (10/100)² = 5000 × 0.01 = ₹50

5. Exam Quick Tips

• Learn A = P(1 + r/100)ⁿ; CI is always A − P.
• For half-yearly, halve the rate and double the time; for quarterly, quarter the rate and quadruple the time.
• The 2-year CI−SI difference is P(r/100)² — a very common one-line question.
• CI equals SI only for the first year when compounded yearly.

Keep revising with the rest of the Maths section:

• All Maths topics
• Simple Interest Formula Cheat Sheet
• Percentage Formula Cheat Sheet

How this was made: Drafted with AI assistance; spot-checked by the editor on 31 October 2026.