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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 ...view middle of the document...

Thus the PVA and FVA equations cannot be applied.

Note: There are three payments (c) and five time periods (t).

Perpetuity

Perpetuity is similar to annuity. The only difference between annuity and perpetuity is the ending period. For annuity, payments last for a certain period, whereas for perpetuity, they continue indefinitely, as represented by (∞).

The equation below is used to calculate present value of perpetuity. It requires only the first payment and interest rate.

where…

* PV(∞) = present value of perpetuity.

* C = the first payment

* r = interest rate per period

For example, an insurance company has just launched a security that will pay $150 indefinitely, starting the first payment next year. How much should this security be worth today if the appropriate return is 10%? Using the time line below, complete the PV(∞) equation.

The equation below is used to calculate present value of perpetuity. It requires only the first payment and interest rate.

* PV(∞) = ?

* C = 150

* r = .10

*A perpetuity is a type of annuity.

Normally, an annuity pays something back each year and then returns your principal at the end of a number of years. A perpetuity gives you a payment each year forever and never gives you your money back. The converge in present value at the length of the annuity increases because, let's face it, getting your principal back in 99 years is pretty close to not getting it back at all. If you don't believe me, play with the present value function in excel.

Differences Between an Annuity & a Perpetuity

Britt Barclay

Christian Barclay is currently an undergraduate in the Farmer School of Business at Miami University of Ohio. He has research experience in the field of chemical engineering and interned this previous summer at the Four Seasons Nile Plaza in Cairo, Egypt. He has written for Demand Studios since May 2009 and has been published on eHow.com and Golflink.com.

By Britt Barclay, eHow Contributor | updated October 25, 2011

Annuities and perpetuities are both types of payment schedules; these schedules are most often plans to settle a debt. Payments on these debts are made at regular intervals. One of these intervals is considered one period. Annuities and perpetuities are used by...

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