An annuity refers to a series of regular payments, each of which is of the same amount. You may make the regular payments, for example to repay a loan or to save up for retirement. You may receive the payments, for example in the case of an investment vehicle in which you put in a large lump sum of money at the beginning and get the annuity payments with interest over time. You can determine the length of an annuity term using the annuity formula.
Find out all the features of the annuity. You need to know the amount of each regular payment (PMT), the interest rate, the length of time between two payments, the amount of money at the beginning of the annuity (present value or PV), and the amount of money at the end of the annuity (future value or FV). For example, at the beginning of a loan, the beginning value is the amount you borrow and the end value after you finish paying it off is zero. With savings, you start with your current balance and the amount of money you want to eventually have.
Divide the annual interest rate by the number of payments per year to get the interest rate that applies each payment period (i). For example, if the annual interest rate is 13.2 percent and the payments occur each month, then the monthly interest rate would be 1.1 percent (from 13.2 percent / 12).
Enter the various figures into the annuity formula: PV = FV (1+i)^N + PMT (1-(1+i)^(-N)) / i). In this formula, N stands for the number of payments you make over the life of the annuity. For example, assume you take out a $13,850 loan and make monthly payments of $500 to pay it off. The monthly interest rate is 1.1 percent. Because you will pay off the loan at the end of the annuity, the future value of this annuity is 0. You will make the following calculations: 13,850 = 500 (1 - (1+0.011)^(-N) / 0.011) 13,850 = 500 (1 - 1.011^(-N) / 0.011) 27.7 = 1 - 1.011^(-N) / 0.011 0.3047 = 1 - 1.011^(-N) 1.011^(-N) = 0.6953
Find the number of payments using a logarithmic function on your calculator. Using the figures from the previous step: -N = ln 0.6953 / ln 1.011 -N = -33.22 N = 33.22
Convert the number of payments into years. In the example, you make the payments monthly and will finish paying the loan off in 33.22 months. This means that the annuity will run for 2.77 years or 2 years and 9 months.
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