# Ordinary Annuity

## What is an 'Ordinary Annuity'

An ordinary annuity is a series of equal payments made at the end of consecutive periods over a fixed length of time. While the payments in an annuity can be made as frequently as every week, in practice, ordinary annuity payments are made monthly, quarterly, semi-annually or annually. The opposite of an ordinary annuity is an annuity due, where payments are made at the beginning of each period.

## BREAKING DOWN 'Ordinary Annuity'

Examples of ordinary annuities are interest payments from bond issuers, which are generally paid semi-annually, and quarterly dividends from a company that has maintained stable payout levels for years. The present value of an ordinary annuity is largely dependent on the prevailing interest rate. Because of the time value of money, rising interest rates reduce the present value of an ordinary annuity, while declining interest rates increase its present value. This is because the value of the annuity is based on the return you can get elsewhere. If you can get a higher interest rate somewhere else, the value of the annuity in question goes down.

## Present Value of Ordinary Annuity Example

The present value formula for an ordinary annuity takes into account three variables. They are:

PMT = the period cash payment

r = the interest rate per period

n = the total number of periods

Given these variables, the present value of an ordinary annuity is:

Present Value = PMT x ((1 - (1 + r) ^ -n ) / r)

For example, if an ordinary annuity pays \$50,000 per year for five years and the interest rate is 7%, the present value would be: Present Value = \$50,000 x ((1 - (1 + 0.07) ^ -5) / 0.07) = \$205,010.

## Present Value of Annuity Due Example

Recall that with an ordinary annuity, the investor receives the payment at the end of the time period. This stands in contrast to an annuity due, where the investor receives the payment at the beginning of the period. This impacts the value of the annuity. The formula for an annuity due is slightly different as follows:

Present Value of Annuity Due= PMT + PMT x ((1 - (1 + r) ^ -(n-1) / r)

If the annuity in the above example was instead an annuity due, the present value of it would be calculated as: Present Value of Annuity Due= \$50,000 + \$50,000 x ((1 - (1 + 0.07) ^ -(5-1) / 0.07) = \$219,360.

All else being equal, an annuity due is always worth more.