## Ordinary Annuity

An ordinary annuity, also known as a deferred annuity, is a series of equal payments made at the end of each period over a certain amount of time. The period could be monthly, quarterly, semi-annually, or annually.

Annuities are used in finance to model various financial arrangements and products, such as mortgage payments, retirement plans, insurance products, and more.

In an ordinary annuity, since payments occur at the end of each period, interest does not accumulate on the last payment, as it is assumed to be taken out immediately. This differs from an annuity due, where payments are made at the beginning of each period, and therefore each payment has the opportunity to earn interest during its respective period.

Here’s a simple formula for calculating the future value (FV) of an ordinary annuity:

FV = P * [(1 + r)^n – 1] / r

Where:

- P is the amount of each annuity payment
- r is the interest rate per period
- n is the total number of periods

The present value (PV) of an ordinary annuity can be calculated as:

PV = P * [1 – (1 + r)^-n] / r

Here, the same parameters apply as above.

## Example of an Ordinary Annuity

Let’s say you are planning to retire in 20 years, and you decide to invest $5,000 per year into a retirement account that generates an annual return of 5%. This is an example of an ordinary annuity because the $5,000 investment is made at the end of each year.

Using the formula for the future value of an ordinary annuity:

FV = P * [(1 + r)^n – 1] / r

we can calculate the total value of your investment after 20 years.

FV = $5,000 * [(1 + 0.05)^20 – 1] / 0.05

FV = $5,000 * [2.6533 – 1] / 0.05

FV = $5,000 * 33.066

FV = $165,330

So, after 20 years of making a $5,000 investment at the end of each year, and with an annual interest rate of 5%, your retirement account would grow to $165,330.

Note: This calculation assumes that interest is compounded annually, which may not be the case with all investments. Always check the terms of your specific investment for accurate calculations.