Author: Awais Ahmad (


An Annuity is a series of equal payments made at fixed intervals for a specified number of periods. These equal payments are denoted by the PMT and can occur at either the beginning or the end of each period. Future and Present Values of Annuity: Future Value of an Annuity can be calculated, where a series of equal payments are made at a fixed intervals for a specific number of periods. The principle applied here is just like Compounding. However, method of calculating Future Value of Annuity differs in Ordinary Annuity and Annuity Due. Similarly, Present Value of an Annuity can also be calculated by using the principle of Discounting, but the method of calculating Present Value of Annuity differs in Ordinary Annuity and Annuity Due. Types of Annuity: Annuity has following types depending on the period of payment.

1. Ordinary/Deferred Annuity:

If the payments of Annuity occur at the end of each period, it is called Ordinary or Deferred Annuity.

Future Value of Ordinary Annuity:

If equal payments PMT is made at the end of n periods, providing a saving of i, then Future Value of Annuity (FVa or FVAn) can be calculated as:

Present Value of Ordinary Annuity:

If equal payment PMT is made at the end of n periods, providing a saving of i, then Present Value of Annuity PVAn can be calculated as:

2.      Annuity Due

If the payments of Annuity occur at the beginning of each period, such Annuity is called Annuity Due.

Future Value of Annuity Due:

If equal payment PMT is made at the beginning of n periods, providing a saving of i, then Future Value of such Annuity FVAn can be calculated as:

The only difference between Future Value of Deferred Annuity and Annuity Due is that every term of Future Value of Annuity Due is compounded for one extra period, reflecting the fact that each payment for an Annuity Due occurs one period earlier than Ordinary Annuity.

Present Value of Annuity Due:

If equal PMT is made at the beginning of n periods, providing a saving of i, then Present Value of such Annuity PVAn can be calculated as:

The only difference between Present Value of Deferred Annuity and Annuity Due is that every term of Present Value of Annuity Due is discounted for one extra period, reflecting the fact that each payment for an Annuity Due occurs one period earlier than for Ordinary Annuity.

3.      Perpetuity

Some Annuities go on indefinitely, or perpetually, and are called Perpetuities. The Present Value of such Annuities is simple to calculate.


Financial Management – Theory & Practice by Eugene F. Brigham & Michael C. Ehrhardt

Notes on Investment Analysis and Portfolio Management

Lectures of Respectable Teahers

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