# Compound Interest: Basic Concepts, Formulas

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## Compound Interest Formula and Concept

### Compound Interest Meaning

When the amount after the first unit of time becomes the Principal for the second unit of time and so on, after fixing a certain unit of time, say yearly or half-yearly or quarterly to settle the previous amount.

This difference between the Amount and the Principal after a specified period is called Compound Interest.

### Important Compound Interest Formula

• When the interest is compounded annually –

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

• When the interest is compounded Half-yearly –

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

• When the interest is compounded quarterly –

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

• When the interest is compounded annually but time is in the fraction, say $3\frac { 3 }{ 5 }$

Amount = $P{ \left( 1+\frac { R }{ 100 } \right) }^{ 3 }\times \left( 1+\frac { 3R/5 }{ 100 } \right)$

• When rates are different for different years, say ${ R }_{ 1 },{ R }_{ 2 },{ R }_{ 3 }$ for Ist, 2nd, and 3rd year respectively-

Amount = $P\left( 1+\frac { { R }_{ 1 } }{ 100 } \right) \left( 1+\frac { { R }_{ 2 } }{ 100 } \right) \left( 1+\frac { { R }_{ 3 } }{ 100 } \right)$

#### Examples-

Q-1. Find the compound interest on Rs. 7500 at 4% p.a for two years compounded annually?

Solution-

Method-1(Using Formula)

Amount = [7500×(1 + 4/100)²] = (7500 × 26/25 × 26/25) = Rs. 8112

CI = 8112 – 7500 = Rs. 612

Method-2

Interest for first year since rate is annually, where P =7500, R = 4%, T = 1 year

Interest = (PRT/100) = (7500×4×1)/100 = 300

Now for the 2nd term

P = 7500 + 300 = 7800, R = 4%, T = 1 year

Interest = PRT/100 = (7800×4×1)/100 = 312

So, the total interest is 300 + 312 = Rs. 612