Ordinary annuities are fixed-size investments that yield interest-bearing payments over a preset time. The first payment is received at the end of the first period of time. Using an annuity worksheet, you can calculate the present value, the future value, and/or regular payment amounts.
Determine one of the three variables of interest: the investment’s present value, the investment’s future value, and/or the investment’s periodic payment. Call these variables PV, FV, and p.
Determine the rate of interest at which the annuity will be invested, and call this variable i, for interest. Interest is usually expressed as an annual rate.
Determine the number of years for which the annuity will make payments Call this number n, for the number of payments.
Calculate the yearly annuity payment using the following formula:
p = [PV x i]/[1-(1+i)^-n]. For example, if the present value of the annuity is $25,000 at a 10 percent annual rate of interest, and it will pay for five years, you’ll receive a yearly payment of [25,000 x .10]/[1-(1+.10)^-5] = $6,594.94.
Calculate the future value of the annuity using the following formula:
FV = p x [(1 + i)^n – 1]/i. For example, if the annuity will pay $6,594.94 per year for five years at a 10 percent annual rate of interest, the future value will be 6,594.94 x [(1.1)^5 – 1]/.10 = $40,262.77.
Calculate the present value of the annuity using the following formula:
PV = p x [1 – (1 + i)^-n]/i. For example, if the annuity will pay $6,594.94 per year for five years at a 10 percent annual rate of interest, the present value is 6,594.94 x [1 – (1.1)^-5]/.10 = $25,000.
Finally, the present value and the future value can be calculated from each other:
FV = PV x (1 + i)^n, so that 25,000 x (1.1)^5 = $40,262.77
PV = FV x (1 + i)^-n, so that 40,262.77 x (1.1)^-5 = $25,000
Calculating n is more difficult, although it can be done using the logarithmic reduction of the annuity formula. Fortunately, n is almost always given to you. On the other hand, i is actually impossible to calculate explicitly, so if you want to calculate the implicit interest rate of an annuity given the investment and payment amounts, you’ll need to use a financial calculator or manually interpolate to estimate it. Like n, i will almost always be given as well.
- Jupiterimages/Photos.com/Getty Images