Calculates the payments for a loan or annuity with constant payments and a constant interest rate.

**PMT Formula:**

PMT=

IF Rate = 0 THEN

(-Pv -Fv) / Nper

ELSE

(Fv + Pv * (1 + Rate)^{Nper}) * Rate / ((1 - (1 + Rate)^{Nper})* (1 + Rate * Type))

where *Type *is either 0 for payments at the end of each period, 1 for payments at the beginning of each period.

## Syntax

PMT(r, n, p, [f], [t])

where:

- r: Number: Interest rate per period
- n: Number: The number of periods
- p: Number: Present value or the initial investment. Cash outflows such as investments are entered as negative numbers. If you are taking out a loan, this is a cash inflow so is entered as a positive number
- f: Number: future or residual value (optional)
- v: Number: when the payments are made. 0 or omitted means payments are made at the end of each period, non-zero means payments are made at the start of each period (optional)

## Format

Input Format | Output Format |
---|---|

r: Rate: Number (percentage) n: Nper: Number p: Pv: Number f: Fv: Number v: Type: Number (binary) |
Number |

## Arguments

The function uses the following arguments:

- r: Numeric line item, property, or expression - percentage
- n: Numeric line item, property, or expression
- p: Numeric line item, property, or expression
- [f]: Numeric line item, property, or expression (optional)
- [t]: Numeric line item, property, or expression - binary (optional)

## Constraints

The function has the following constraints:

- Cash outflows are entered as negative numbers, cash inflows as positive numbers.

## Excel equivalent

## Example

*Contract 1* represents a cash investment *Pv* of 10000 at the end of period 1. The duration of the investment *Nper* is *24* months at which point the residual value *Fv* of *4000* is returned as a lump sum. The monthly interest rate *Rate* is *1.0%* per period (approx 12.0 % per annum).

PMT calculates the *24* equal monthly payments of *322.44* to achieve this rate of interest.

PMT(Rate, Nper, Pv, Fv, Type)

*Contract 5* represents a loan of *20000*. With an interest rate of *0.5%* per period, *24* equal periodic payments of *886.41* are needed.