Compound Interest: Concepts, Formulas, and Clear Examples

CI grows as $A = P(1+r)^t$ where $r=R/100$ per compounding period. Each period’s interest earns interest—exponential, not linear like SI.

Watch compounding frequency: half-yearly → rate $R/2$ per half-year, periods $2T$. Questions often ask CI−SI difference or depreciation $(1-r)^t$.

Memorize: for 2 years, CI−SI $= P(r^2)$ when annual compounding.

Amount and CI

Annual

$$A = P\left(1 + \frac{R}{100}\right)^T$$

CI

$$\text{CI} = A - P$$

Example — Two years 10%

$P=5000$, $R=10\%$, $T=2$. $A=5000(1.1)^2=6050$. CI = 1050. SI = 1000; extra 50 = interest on first year’s 500.

Half-yearly / quarterly

Half-yearly

$$A = P\left(1 + \frac{R/2}{100}\right)^{2T}$$

Quarterly

$$A = P\left(1 + \frac{R/4}{100}\right)^{4T}$$

CI minus SI

2 years gap

$$\text{CI} - \text{SI} = P\left(\frac{R}{100}\right)^2$$

Depreciation

Value after decay

$$V = P\left(1 - \frac{R}{100}\right)^T$$

Doubling time

• If amount doubles, $(1+R/100)^T = 2$. Solve for $R$ or $T$ from options.

Effective rate

m periods/year

$$r_{\text{eff}} = \left(1 + \frac{R}{m\cdot100}\right)^m - 1$$

Step-by-step method for exam questions

1. Extract P, R, T and compounding type.
2. Convert to per-period rate and period count.
3. Compute $A=P(1+r)^n$.
4. CI = A − P; compare SI if asked.
5. Use 2-year difference shortcut when applicable.
6. Match closest option; watch rounding.

Formula cheat sheet

Frequently asked questions

First year CI vs SI?

Same for identical P, R, T=1 year.

Higher compounding frequency?

Higher effective return for same nominal R.

Common trap?

Using SI formula $PRT/100$ inside an exponent.

Fractional years?

Align period count (e.g., 18 months half-yearly → 3 periods).

Practice on this platform

Use 4 practice sets (10 MCQs, detailed solution after each answer) and 2 timed mocks (20 minutes) on this topic to convert formulas into speed and accuracy.