Annuity & Perpetuity

Annuity

Annuity is a special case of multiple cash flows where:

* The cash flows are equal for a fixed period of time.

* The cash flows are at the end of each period.

The equal amount of cash flows is called annuity payment or payment (C).

You can solve an annuity problem the same way as multiple cash flows, calculating the value of each cash flow and sum all values. However, this can be quite tedious especially when dealing with long series of annuity payments. Fortunately, future and present values of annuity payments can be calculated from the following equations:

    or    

Where:

* FVA = future value of annuity

* PVA = present value of annuity

* C = amount of equal payments

* r = interest rate per period

* t = number of payments (number of time periods)

For example, you plan to save $200 per year for the next five years for your new car's down payment. How much will you have as the down payment if you earn 10% interest rate on the savings? Using the time line below, we can fill in the missing information of the equation to solve for FVA:

* FVA = ?

* C = 200

* r = .10

* t = 5

In order to call a series of cash flows an annuity and use the PVA and FVA equations, the following must be true:

1. All payments must be equal and consecutive.

2. Payments last for a certain period.

3. The first payment starts one period from the beginning of the time line (time period for PV).

4. The last payment is at the end of time line (time period for FV).

A quick way to check whether a series of payments is annuity is that the number of payments must be the same as the number of time periods. In the previous example, there are 5 payments (C) which are equal to 5 periods (years). Therefore, the problem can be called annuity.

The series of payments displayed in the time line below, however, cannot be called annuity because the number of payments (C) is not the same as the number of time periods (t)....