Education Technology

# Knowledge Base

## Solution 21852: Calculating the Present Value of a Perpetuity (Infinite Annuity) on a TI-83 Family, TI-84 Plus Family, or TI-Nspire™ Handheld in TI-84 Plus Mode.

### How can I calculate the present value of a perpetuity (infinite annuity) on a TI-83 family, TI-84 Plus family, or TI-Nspire handheld in TI-84 Plus mode?

Sometimes when dealing with annuities, there are those that pay forever instead of for a specific period of time. Hence, they are called perpetuity or infinite annuities. Since these units do not have a way to specify an infinite number of periods for N, the calculation involves the fact that the present value of a cash flow far enough into the future is going to be approximately $0. This means that futuristic-ally the cash flows no longer add anything to the present value. Therefore, selecting a large number of payments yields a close approximation to a perpetuity. For example, the payment is$5,000 per year and the interest rate is 9% annually. Since it is a perpetuity, the user can select 500 as N. First, access the TVM solver by pressing [APPS] [ENTER] [ENTER]. On the TI-83, press [2nd] [FINANCE] [ENTER]. Input the following:

Next, place the cursor next to PV and press [ALPHA] [SOLVE] to compute the present value:

The present value is \$-55,555.56.

Note: There is not a way to find the future value of a perpetuity because the cash flows never end.

Please see the TI-83 Plus Family and TI-84 Plus Family guidebooks for additional information.

TI-Nspire handheld in TI-84 Plus mode users may refer to the TI-84 Plus family guidebook.