# Compound Interest

Money is said to be lent at compound interest if the interest is not paid as soon as it falls due but is added to the principal after a fixed period, so that the amounts at the end of the period becomes the principal for the next period.

## Formulas:

If, P = Principal.R = Rate of interest.(%)

T = Time.

Amount = Principal + Interest.

Compound interest = Amount - P

- To calculate compound interest Annually:
Amount for compound interest = P 1 + R ^{T}100 or

Compound interest = P 1 + R ^{T}- 1 100

- If the interest is payable half-yearly:
- If the interest is payable Quarterly:
- If interest is payable annually but time is in fraction:
- If interest rates for successive years are different:

Amount | = | P | 1 + | ( R / 2 ) | ^{2T} |
||

100 |

Amount | = | P | 1 + | ( R / 4 ) | ^{4T} |
||

100 |

Let, Time | = | 5 | 2 | years. |

3 |

Amount | = | P | 1 + | R | ^{5} |
X | 1 + | (2/3) R | ||||

100 | 100 |

Let, r_{1},r_{2},r_{3}...are the rates for successive years.

Amount | = | P | 1 + | r_{1} |
X | 1 + | r_{2} |
X | 1 + | r_{3} |
||||||

100 | 100 | 100 |