# What Is the Present Value of an Annuity Formula and What Are Annuities?

If you already know the concept of Perpetuities, the concept of Annuities is very easy. It's very similar to Perpetuities, only that the payments are not forever. Instead of forever, these payments come in only for a fixed time period.

Let's say I've saved you a piece of paper or certificate, and it promised that I would pay you \$ 10 per year for exactly 12 years, and then I would stop paying you immediately after that. Is this still a "perpetuity"? It still consist of regular payments of equal amounts, just like a perpetuity, but it is not forever; it has a limited time period. So in this case, it's not called a perpetuity, but an "annuity."

So now, just like in the case of a perpetuity, an important question now is … how much are you willing to pay me for that piece of paper? How much are you willing to pay for this "annuity"?

For this, you would use the Present Value of an Annuity Formula. For general managers, there's no need to know the actual step by step process on calculating this, as it can easily be done by accountants or by free calculators online as well as smartphone apps. However, if you need to learn the process yourself, you can watch tons of free online tutorial videos from many different websites as well as YouTube.

Real-Life Application

Let's say you are offered to invest your severance pay (or return pay, or similar lump sum) of \$ 10,000 with a pension company or investment company, and they promise to pay you \$ 600 / year for 30 years. An ordinary person may think it's a good deal because \$ 600 / year x 30 years = \$ 18,000, which will be much more than the original \$ 10,000 investment.

However, using the Present Value of an Annuity Formula, you will find that the "fair value" of this annuity is actually only \$ 9,223 if interest rates are at 5% … and that you are there "overpaying" if you pay anything more than \$ 9,223. In other words, if you pay anything more than \$ 9,223, then you're just as good or even better off putting your money in the bank instead, and earning interest from the bank (or other "risk-free" investment). At \$ 9,223, the rate of return of your investment / pension will be exactly equal to the rate of return of putting your money in the bank. If you pay more than \$ 9,223 for your investment, then your investment rate of return will be lower than your return from the bank.