# Payment (PMT) Calculator

LAST UPDATE: October 8th, 2019

### What is a Payment?

Payment (PMT) is a regular payment into or out of a financial stream over a period of time.

### PMT Formula – How the Payment amount is calculated

Payments calculate through a financial formula used to determine the time value of money.

$\text{PMT}=(\text{PV} + \frac{\text{PV} + \text{FV}}{(1 + \text{r})^{\text{n}}-1})\times \frac{-\text{r}}{1 + \text{b}}$

Where:

• PV or “Present Value” is the value of the starting sum or initial investment.
• FV or “Future Value” is the value of the final amount.
• r or “Rate” is the rate used per compounding period.
• n or “Number of Periods” is the number of periods of compounding (and payments) that occur.
• b or “Rate if Payments at the Beginning” if the payments occur at the end of each period, “b” = 0. If the payments occur at the beginning of each period, “b” = “r”.
• PMT or “Payment” is the regular payment each compounding period.

### Example

What payment is needed to get from a present value of $1000 to a future value of$2000 using a rate of return of 2.2% over 10 periods? Payments are at the begining of each compounding period.

$\text{PMT}=(1,000 + \frac{1,000 + 2,000}{(1 + 0.022)^{10}-1})\times \frac{-0.022}{1 + 0.022}$

$\text{PMT}=(1,000 + \frac{3,000}{(1.022)^{10}-1})\times \frac{-0.022}{1.022}$

$\text{PMT}=(1,000 + \frac{3,000}{1.243108-1})\times -0.0215264$

$\text{PMT}=(1,000 + \frac{3,000}{0.243108})\times -0.0215264$

$\text{PMT}=(1,000 + 12,340.194481)\times -0.0215264$

$\text{PMT}=13,340.194481\times -0.0215264$

$\text{PMT}=-287.17$

### Sources and External Resources

• Wikipedia – Time Value of Money – Wikipedia’s entry on the founding principles behind time value of money, including calculating a payment.
• getobjects.com (archived via archive.org) – Time Value of Money (TVM) Formulas – A collection of time value of money formulas. Includes formulas for other calculations such as number of periods and rate of return as well.