When you invest in an annuity, you put a fixed amount of money into an investment vehicle at the beginning or end of a fixed period of time. At the end of the duration of investment, you get the maturity value of an annuity, which is the amount you invested plus interest. To find the amount of interest the annuity, you must first calculate the value of annuity due, then subtract the amount of money you invested. To perform this calculation, you need to know the amount of money per payment, payment amount, length of each payment period and interest rates.
You can easily understand the concepts behind calculating annuity rates if you know the basic compound interest. When you invest money in the account of the accumulated compound interest, you earn interest on the principal and interest that has accumulated. In other words, the amount of interest you earn at the end of each period increases more of your money sitting in investment vehicles.
For example, if you have $ 100 dollars to earn interest of 5 percent per year, at the end of the first year, you'll have $ 105 USD. At the end of the second year, you will earn 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 will grow to $ $ 5.25 in the second year. The amount of interest you earn increases with time, and you can calculate the value of your investment at the end of each period by using the following formula: initial investment x (1 + interest rate per period) the number of periods. In our example, the calculation for the second year are: 100 x (1 + 0.05) 2 = 110.25.
With annuities, you need to perform more sophisticated calculations as you add money each period. You can use the compound interest formula to calculate each payment separately, but the calculations long as it could become unmanageable. For easier calculation, using this formula: the value of the annuity payment due per period = x [((1 + interest rate per period) the number of periods - 1) / interest rate per period]. After finding the maturity value, you should use only simple formula to find interest annuity: the maturity value - (the number of payments per period x period).
Say that you invest $ 100 USD by the end of each 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 numbers into the formula: 100 x [((1 + .05) 8-1) / 0.05] = 954.91. At the end of eight years, having contributed $ 100 USD at the end of each year, you'll have $ 954.91 USD. In other words, in this case, your interest annuity for eight years is 954.91 - (8 x 100) = 154.91, or $ 154.91 USD.
In this example, we assume that you make payments at the end of each period, which is the basic annuity computation. However, some annuities have a payment at the beginning of each period. In such cases, the formula for calculating the value of annuity due to: the payment per period x [((1 + interest rate per period) the number of periods + 1 - 1) / interest rate per period]. Also, we assume that the annuity is an investment, but some take the form of the annuity promises to make payments over a given period is not - a lottery or a pension, for example. When calculating the real annuity, you also often have to make assumptions about interest rates, because interest rates fluctuate.