An annuity is a type of contract between an individual and an insurer.
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 annuity maturity value, which is the amount invested plus interest. To know the interest amount of the annuity, you first need to calculate the maturity amount of the annuity and then subtract it from the amount 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 can easily understand the concept behind calculating annuity interest if you know basic compound interest. When you invest money in an account that accrues compound interest, you earn interest on both the principal and previously accrued interest. In other words, the amount of interest you receive at the end of each period increases the longer your money stays in the investment vehicle.
For example, if you have $100 USD that earns 5% interest per year, at the end of the first year, you will have $105. At the end of the second year, you will receive 5% interest on $105 USD, which means which will have $110.25 USD. Your money will only grow by $5 USD in the first year, but will increase by $5.25 USD in the second year. The amount of interest you earn increases over 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 have to do more sophisticated calculations as you add money each period. You can use the compound interest formula to calculate each payment separately, but these lengthy calculations can become unmanageable. For easier calculations, use this formula: annuity maturity amount = payment per period x [((1 + taxa de juros por período) número de períodos – 1) / taxa de juros por período]. Once you find the maturity amount, you should just use this simple formula to find the annuity interest: maturity amount – (number of periods x payment per period).
Let’s say you invest $100 USD at the end of each year in an annuity that has a life of eight years at an interest rate of 5% per annum. 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 base annuity calculation. However, some annuities have payments at the beginning of each period. In this case, the formula for calculating the annuity maturity amount becomes: payment per period x [((1 + taxa de juros por período) número de períodos + 1 – 1) / taxa de juros por período]. Also, we assume the annuity is an investment, but some annuities take the form of a promise to give you payments over a certain period of time – lotteries or pensions, for example. When calculating actual annuities, it is often also necessary to make an assumption about the interest rate, because the interest rate fluctuates.