# What is an annuity worth?

### First of all, what IS an annuity?

An annuity is a fixed-income investment, where you pay a lump sum up front and receive steady payments on a regular basis. The payments will be more than typical savings accounts or CDs because you lose the principal. You basically get paid the typical interest rate for savings, plus some of your principal too.

To figure out how much will need to be invested to receive a certain payment, you can use the Present Value of an Annuity formula. Basically it figures out how much money you are loaning the bank (or insurance company) in return for regular repayment.

$$A=\frac{P}{r}*[1-(1+r)^{-t}]$$

A is the total amount of the annuity, P is the payment, r is the interest rate, and t is the number of periods. Make sure to be consistent with the time period - if you use months, you have to divide the annual interest rate by 12 and multiply the number of years by 12.

Here's an example: Suppose Mary wants to purchase an annuity that pays $1000/month for the next 20 years. The interest rate on this annuity is 6%. How much will she have to pay now to secure such an annuity? $$A=\frac{1000}{\frac{.06}{12}}*[1-(1+\frac{.06}{12})^{20*12}]=139,581$$ She has to pay$139,581 today to receive guaranteed payments of $1000 a month for the next 20 years (a total of$240,000). The bank or insurance company still makes money by investing that lump sum at a higher rate of return than they are paying out to Mary.

This type of annuity is a fixed annuity because it pays a set payment every month. It is also a fixed-period annuity because it pays for 20 years. Other annuities have variable rates depending on the performance of bonds or stocks held by the institution. Some pay for the rest of your life, however long or short that may be.

Often, insurance companies handle annuities because they are very good at knowing how long people will live. If their customers all lived too long, they would have to keep paying annuities!