# Interest Rate

## Interest rate is the cost of money.

*Interest *is the cost of money and is measured by the * interest rate* where* *

interest rate = cost of having money available for use

The interest rate is a percentage that is periodically added to an amount of money over a specified length of time. If money is borrowed the interest rate is the percentage of the borrowed amount that is paid to the borrower as a compensation for the use of the borrowed property.

Interest reflects that

- money available today has a greater value that money received in the future

The future value of a present amount of value can be expressed as

F = P (1 + i)^{n}(1)

where

F = future value

P = present value

i = interest rate per period

n = number of interest periods

### Example - Accumulated Value

The accumulated value of an amount of present value *1* today with interest rate *10%* in a *10 years* period can be expressed as

Year | Accumulated Value |
---|---|

0 | 1 |

1 | 1.1 |

2 | 1.21 |

3 | 1.33 |

4 | 1.46 |

5 | 1.61 |

6 | 1.77 |

7 | 1.94 |

8 | 2.14 |

9 | 2.36 |

10 | 2.59 |

An amount of *500* will accumulate with the factor *2.14* in *8 years* - or

* F = 2.14 (500)*

* = 1070*

### Future Value of Present Money due to Interest Rate - Calculator Table

This calculated table visualizes the increase in future value of present money due to interest rate and time.

*Present Value of Money*

* Start Year*

* End Year*

* Max. Interest Rate (%)*

Download and print Future Value of Present Payment chart

### Interest Rate - Online Calculator

*P - Present value*

*i - interest rate per period (%)*

*n - number of periods*

### Finding Unknown Interest Rate

If a single payment *P* shall produce a future value *F* after *n* annual compounding periods, the per annum decimal interest rate can be calculated as

*i = (F / P) ^{1/n} - 1 (2)*

#### Example - Finding Interest Rate

A single payment of *100* today shall grow to *120* in 5 years. The required interest rate can be calculated as

*i = (120 / 100) ^{1/5} - 1 *

* = 0.037*

* = 3.7 %*