Simple & Compound Interest — Quant Aptitude Questions & Formulas

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Simple & Compound Interest

1. The Two Engines

	Interest earned	Amount after $n$ years
Simple	$SI=\dfrac{P\,R\,T}{100}$	$A=P\left(1+\dfrac{RT}{100}\right)$
Compound	$CI=A-P$	$A=P\left(1+\dfrac{R}{100}\right)^{n}$

Simple interest grows linearly (the same amount every year); compound interest grows geometrically (each year earns on the previous year's total).

2. Compounding More Than Once a Year

Halve the rate and double the time for half-yearly, quarter it and quadruple it for quarterly:

A=P\left(1+\frac{R}{2\times100}\right)^{2n}\qquad A=P\left(1+\frac{R}{4\times100}\right)^{4n}

3. The CI - SI Gap

For the same

P

R

and

T

the difference is a standard shortcut:

\text{2 years: } P\left(\frac{R}{100}\right)^{2}\qquad\text{3 years: } P\left(\frac{R}{100}\right)^{2}\!\left(\frac{R}{100}+3\right)

4. Common Patterns

Doubling/trebling under SI: money doubles when

SI=P

, i.e.

RT=100

Equal instalments: discount each instalment back to the present and sum them.

Successive rates

r_1,r_2

: net factor is - never add the rates.