# 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 period. Although payments in a regular annuity can be made as often as weekly, in practice they are usually made monthly, quarterly, semi-annually or annually. The opposite of an ordinary annuity is a due annuity, in which payments are made at the start of each period.

### Key points to remember

• An ordinary annuity is a series of regular payments made at the end of each period, such as monthly or quarterly.
• In an annuity due, however, payments are made at the start of each period.
• Constant quarterly stock dividends are an example of an ordinary annuity; the monthly rent is an example of an annuity due.

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## How does an ordinary annuity work

Examples of ordinary annuities are bond interest payments, which are usually made semi-annually, and quarterly dividends from a stock that has maintained stable payment levels for years. The present value of an ordinary annuity largely depends on the prevailing interest rate.

Because of the time value of money, rising interest rates reduce the present value of an ordinary annuity, while falling interest rates increase its present value. This is because the value of the annuity is based on the return that your money could earn elsewhere. If you can get a higher interest rate elsewhere, the value of the annuity will decrease.

## Present value of an example of an ordinary annuity

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

• PMT = cash payment period
• r = the interest rate per period
• n = the total number of periods

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

Current value = PMT x ((1 – (1 + r) ^ -n) / r)

For example, if a regular annuity pays \$ 50,000 a 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.

An ordinary annuity will have a present value lower than a due annuity, all other things being equal.

## Present value of an example annuity maturity

Remember that with an ordinary annuity, the investor receives the payment at the end of the period. This contrasts with an annuity due, in which the investor receives payment at the start of the period. A common example is rent, where the tenant usually pays the landlord in advance for the coming month. This difference in payment schedule affects the value of the annuity. The formula for an annuity due is as follows:

Present value of the rent due = PMT + PMT x ((1 – (1 + r) ^ – (n-1) / r)

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

All other things being equal, an annuity due is always worth more than an ordinary annuity.