# Ordinary Annuity

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## Definition of 'Ordinary Annuity'

An ordinary annuity is a series of equal payments made at regular intervals for a fixed period of time. The payments can be made at the beginning of each period (an annuity due) or at the end of each period (an ordinary annuity). The present value of an ordinary annuity is the sum of the present values of the individual payments, discounted at a given interest rate.

The formula for the present value of an ordinary annuity is:

```
PV = A * [1 - (1 + r)-n] / r
```

where:

* PV is the present value of the annuity
* A is the amount of each payment
* r is the interest rate
* n is the number of payments

For example, if you want to know the present value of an annuity that pays \$100 per month for 10 years at an interest rate of 5%, you would use the following formula:

```
PV = \$100 * [1 - (1 + 0.05)-10] / 0.05 = \$613.91
```

This means that the present value of the annuity is \$613.91.

The future value of an ordinary annuity is the sum of the future values of the individual payments, compounded at a given interest rate.

The formula for the future value of an ordinary annuity is:

```
FV = A * [(1 + r)n - 1] / r
```

where:

* FV is the future value of the annuity
* A is the amount of each payment
* r is the interest rate
* n is the number of payments

For example, if you want to know the future value of an annuity that pays \$100 per month for 10 years at an interest rate of 5%, you would use the following formula:

```
FV = \$100 * [(1 + 0.05)10 - 1] / 0.05 = \$1,744.94
```

This means that the future value of the annuity is \$1,744.94.

Ordinary annuities are often used to fund retirement savings. The payments can be used to cover living expenses, or they can be invested to grow a retirement nest egg.

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