# Calculate Annuity Payment – Funding an Annuity

Posted by Professor Cram in Annuities

## Annuities and Annuity Payments

Many people add to a retirement account at regular intervals through payroll withholding. You may have a savings goal. Solving for an annuity payment is one way to figure out how much you should be saving in order to meet your goal. First, let’s define our terms.

An **annuity** is a stream of payments made through time. A stream of equal payments at equal time intervals is a **fixed annuity**. If those payments are made at the end of each time period (month, quarter, year, etc…) it is an **Ordinary Annuity**. If the payments are due at the beginning of each period, it is an **Annuity Due**.

The payment **amount**, interest **rate**, and **number** of payments all contribute to the **future value** of the annuity. Any annuity calculation has these four variables, and with any three you can find the fourth.

The formula and example below calculates the periodic payment required for an ordinary annuity, with a given interest rate and number of payments (periods), in order to achieve a desired future value. This assumes a starting value of zero.

This formula can also be manipulated to calculate the payments from an existing sum, which would find the payouts that would draw the annuity down to an ending value of zero.

## Formula to Calculate the Payment Amount of an Ordinary Annuity

**PMT = FV(OA) / [((1 + i) ^{n }**

**- 1) / i ]**where:

**FV(OA)**, or Future Value of Ordinary Annuity: the value of the annuity at time t=0**PMT**: Payment amount (value) of the individual payments in each period**i**: periodic interest rate that gets compounded for each period of time(periodic rate may be determined by dividing an annual rate by the number of periods in a year)**n**: number of peroids (same as the number of payments)

## Calculate Annuity Payment: Funding an Ordinary Annuity

Calculate the payment required for an ordinary annuity with a step by step example using your values for the periodic interest rate, number of periods, and future value.

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I am 50 years old and will retire in 10 years. I expect to live for 25 years after retirement, until I am 85. I wants a fixed retirement income that has the same purchasing power at the timeI retire as $50,000 has today. (The real value of his retirement income will decline annually after I retires.) My retirement income will begin the day I retire, 10 years from today; and I will then receive 24 additional annual payments. Annual inflation is expected to be 5%. I currently have $125,000 saved, and I expect to earn 10% annually on my savings. How much must I save during each of the next 10 years (end-of-year deposits) to meet his retirement goal?