**Compound Interest Formula and Concept**

**Compound Interest Meaning**

**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