# Payment (PMT) Calculator

LAST UPDATE: September 25th, 2020

## Definition – What is a Payment?

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

## Formula – How the Payment amount is calculated

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

PMT = (PV x ((PV + FV) ÷ ((1 + r)n-1)) x (-r ÷ (1 + 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.

PMT = (1000 + ((1000 + 2000) ÷ ((1 + 0.022)10-1)) x (-0.022 ÷ (1 + 0.022))

PMT = (1000 + (3000 ÷ (1.02210-1)) x (-0.022 ÷ 1.022)

PMT = (1000 + (3000 ÷ (1.243108 – 1)) x -0.0215264

PMT = (1000 + (3000 ÷ 0.243108) x -0.0215264

PMT = (1000 + 12340.194481) x -0.0215264

PMT = 13340.194481 x -0.0215264

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.