## 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.

## Compound Interest Terms

P = Principal.

R = Rate of interest (%).

T = Time.

## Compound Interest Formulas

Amount = Principal + Interest.

Compound interest = Amount – P

## Formula: To calculate Compound Interest Annually

Amount for compound interest | = | P | 1 + | R | ^{T} |
||

100 |

Compound interest | = | P | 1 + | R | ^{T} |
– 1 | ||||

100 |

## Formula: Compound Interest is Payable Half-Yearly

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

100 |

## Formula: Compound Interest is Payable Quarterly

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

100 |

## Formula: Compound Interest is Payable Annually but time is in Fraction

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

3 |

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

100 | 100 |

## Formula: If Compound Interest rates for Successive Years are Different

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 |