Annuities

An Annuity is a cash flow stream which adheres to a specific pattern. Namely, an Annuity is a cash flow stream in which the cash flows are level (i.e., all of the cash flows are equal) and the cash flows occur at a regular interval. The annuity cash flows are called annuity payments or simply payments. Thus, the following cash flow stream is an annuity.

Figure 1

While, the following cash flow stream is not an annuity because the payments do not occur at a regular interval.

Figure 2

When a cash flow stream is of the form given in Figure 1, i.e., an annuity, the process of finding the Present Value or Future Value of the cash flow stream is greatly simplified.

Present Value of an Annuity

The Present Value of an Annuity is equal to the sum of the present values of the annuity payments. This can be found in one step through the use of the following equation:

where

• PVA = The Present Value of the Annuity
• PMT = The Annuity Payment
• r = The Interest or Discount Rate
• t = The Number of Years (also the Number of Annuity Payments)

Consider the annuity of $100 per year for five years given in Figure 1. If the discount rate is equal to 10%, then the Present Value of the Annuity can be found as follows:

Present Value of the Annuity

Future Value of an Annuity

The Future Value of an Annuity is calculated at the end of the period in which the last annuity payment occurs. The Future Value of the Annuity is equal to the sum of the future values of the individual annuity payments at that time. Thus, the future value of a five year annuity is computed at the end of year five. This can be found in one step through the use of the following equation:

where

• FVA = The Present Value of the Annuity
• PMT = The Annuity Payment
• r = The Interest or Discount Rate
• t = The Number of Years (also the Number of Annuity Payments)

Consider the annuity of $100 per year for five years given in Figure 1. If the discount rate is equal to 10%, then the Future Value of this Annuity at the end of period five can be found as follows:

Future Value of the Annuity