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