When you invest in an annuity, you put a fixed amount of money into an investment vehicle at the beginning or end of several fixed time periods. At the end of the investment duration, you get the maturity value of the annuity, which is the amount you invested plus interest. To find the amount of annuity interest, you first need to calculate the maturity value of the annuity, then subtract it by the amount of money you invested. To do these calculations, you need to know the amount of money per payment, the number of payments, the length of each payment period and the interest rate.
You easily can understand the concept behind calculating annuity interest if you know basic compound interest. When you invest money in an account that accumulates compound interest, you get interest on the principal and the previously accumulated interest. In other words, the amount of interest you get at the end of each period increases the longer your money sits in the investment vehicle.
For example, if you have $100 US Dollars that is earning 5 percent interest annually, at the end of the first year, you will have $105 USD. At the end of the second year, you will get 5 percent interest on $105 USD, which means that you will have $110.25 USD. Your money will grow by only $5 USD in the first year, but it will grow by $5.25 USD in the second year. The amount of interest you get increases with time, and you can calculate the value of your investment at the end of any period using the following formula: initial investment x (1 + interest rate per period)^{number of periods}. In our example, the calculation for the second year is: 100 x (1 + 0.05)^{2} = 110.25.
With annuities, you need to carry out more sophisticated calculations because you add money each period. You could use the compound interest formula to calculate each payment separately, but such long calculations could become unmanageable. For easier calculations, use this formula: maturity value of annuity = payment per period x [((1+interest rate per period)^{number of periods} - 1) / interest rate per period]. After finding the maturity value, you have to use only this simple formula to find the annuity interest: maturity value - (number of periods x payment per period).
Let's say that you invest $100 USD at the end of each year into an annuity that has a life of eight years at an interest rate of 5 percent per year. You can calculate the maturity value by plugging the numbers into the formula: 100 x [((1 + 0.05)^{8} - 1) / 0.05] = 954.91. At the end of eight years, after contributing $100 USD at the end of each year, you will have $954.91 USD. In other words, in this case, your annuity interest over the eight years will be 954.91 - (8 x 100) = 154.91, or $154.91 USD.
In these examples, we assume that you make payments at the end of each period, which is the basic annuity calculation. However, some annuities have payments at the beginning of each period. In such a case, the formula to calculate the maturity value of annuity becomes: payment per period x [((1 + interest rate per period)^{number of periods + 1} - 1) / interest rate per period]. Also, we assume that the annuity is an investment, but some annuities take the form of a promise to give you payments over a certain period of time instead — lotteries or pensions, for example. When calculating real annuities, you also often have to make an assumption regarding the interest rate, because interest rate fluctuates.