# PMT( ) function

Returns the amount of the periodic payment (principal + interest) required to pay off a loan.

## Syntax

PMT(rate, periods, amount <,type>)

## Parameters

Name | Type | Description |
---|---|---|

rate | numeric |
The interest rate per period. |

periods | numeric |
The total number of payment periods. |

amount | numeric |
The principal amount of the loan. |

type optional |
numeric |
The timing of payments: - 0 – payment at the end of a period
- 1 – payment at the beginning of a period
If omitted, the default value of 0 is used. |

Note

You must use consistent time periods when specifying `rate` and `periods` to ensure that you are specifying interest rate **per period**.

For example:

- for monthly
payments on a two-year loan or investment with interest of 5% per annum, specify 0.05/12
for
`rate`and 2 * 12 for`periods` - for annual payments on
the same loan or investment, specify 0.05 for
`rate`and 2 for`periods`

## Output

Numeric.

## Examples

### Basic examples

Returns 1856.82, the monthly payment (principal + interest) required to pay off a twenty-five year, $275,000 loan at 6.5% per annum, with payments due at the end of the month:

PMT(0.065/12, 12*25, 275000, 0)

Returns 1846.82, the monthly payment (principal + interest) required to pay off the same loan, with payments due at the beginning of the month:

PMT(0.065/12, 12*25, 275000, 1)

### Advanced examples

### Annuity calculations

Annuity calculations involve four variables:

- present value, or future value $21,243.39 and $ 26,973.46 in the examples below
- payment amount per period $1,000.00 in the examples below
- interest rate per period 1% per month in the examples below
- number of periods 24 months in the examples below

If you know the value of three of the variables, you can use an Analytics function to calculate the fourth.

I want to find: | Analytics function to use: |
---|---|

Present value |
PVANNUITY( ) Returns 21243.39: PVANNUITY(0.01, 24, 1000) |

Future value |
FVANNUITY( ) Returns 26973.46: FVANNUITY(0.01, 24, 1000) |

Payment amount per period |
PMT( ) Returns 1000: PMT(0.01, 24, 21243.39) |

Interest rate per period |
RATE( ) Returns 0.00999999 (1%): RATE(24, 1000, 21243.39) |

Number of periods |
NPER( ) Returns 24.00: NPER(0.01, 1000, 21243.39) |

**Annuity formulas**

The formula for calculating the **present value** of an ordinary annuity (payment at the end of a period):

The formula for calculating the **future value** of an ordinary annuity (payment at the end of a period):