# Automatic Compound Interest Calculator

## Usage Instructions

Update any of the input fields and this calculator will automatically return the following

- your interest earned
- your final savings
- the annual percentage yield (APY) which is associated with your annual percentage rate and compounding frequency

Most banks compound interest monthly based on your daily average balance in the preceeding period.

### Compounding Frequency Cheat Sheat

Frequency |
Compounds Per year |

Daily* |
365.25 |

Semi-Weekly |
104 |

Weekly |
52 |

Bi-Weekly |
26 |

Semi-monthly |
24 |

Monthly |
12 |

Bi-Monthly |
6 |

Quarterly |
4 |

Semi-Annually |
2 |

Annually |
1 |

* Most years have 365 days in them. Leap years have 366 days. Some banks accrue daily interest for 360 days per year, an equivalent of 30 days per month.

## Compound Interest Formula

### Future Value of Savings

A = P ( 1 + r / n)^{nt}

### Definitions

- A = amount of savings
- P = original investment
- r = rate of interest, as decimal
- n = compounding periods annually
- t = time in years

Amount of savings = Principal originally invested * (1 + decimal annualized rate of interest / number of compounding periods per year)^{times per year interest is compounded * years invested}

### Interest Earned

Then to figure out the interest earnings you would subtract the original principal from the result.

A = P ( 1 + r / n)^{nt} - P

### Example Math

$1,105.08 = $1,000 ( 1 + 0.0016666667/12) ^{12 * 5}

$1,105.08 - $1,000 = $105.08