# Calculating the Future Value of an Ordinary Annuity

The two main types of annuities that exist are ordinary annuities and annuities due. They are similar in nature, and differ only in the timing of payments in each period. Annuities themselves are investment vehicles/loans exhibiting a “series of equal payments in equal time periods.” With ordinary annuities, payments are made at the end of each time period, whereas with annuities due payments are made at the beginning of each period. This essentially means that when calculating future and present values for a given time period (i.e. five years), calculation of an annuity due will include one more payment period then will an ordinary annuity.

#### Practical Uses and Composition the Future Value

Most annuities are ordinary annuities, and calculating the future value of an ordinary annuity is a useful way to measure how much money one will have in a given number of years, with given equal payments at a specific interest rate.  Annuities are often used for retirement purposes, but the calculation can also be used to determine future/present values mortgages rate as well as other types of loans.  The calculation for the future value of an ordinary annuity is simple, and is just the “sum of the future values of each annuity payment.” The formula is: FV = Annuity Payment(1+int. rate) + Annuity Payment(1+int. rate)^1 + Annuity Payment(1+int. rate)^2 + … + Annuity Payment(1+int. rate)^n, where n equals the number of years of the annuity. What this means in laymen terms is that the current annuity payment is multiplied each period by the compound annual growth rate and then summed in order to obtain the future value. For example, if the annual payment is \$100 and the yearly growth rate is 5%, after one year the annuity payment would be \$105, after two years it would be \$110.25, and after three years it would be \$115.7625. The sum of these three payments is \$331.0125, and this is the future value of the annuity in three years. Because the investment is compounded (earning interest on interest), this future value is greater then if the investment were to simply earn 5% on \$100 every year. This approach would yield a three-year future value of \$315 (\$105*3), which is less than the \$331 that is the true FV using the compounded growth rate.

#### The Difference Between Future and Present Values

Whether a person wants to know how much a specific amount of contributions will be worth in the future or the dollar amount that specific contributions will need to be in order to achieve a pre-determined future amount will determine whether one wants to calculate the future value or present value of an annuity. The formula for the present value of an ordinary annuity is: [1-1/(1+int. rate)^n]/int. rate.

#### Calculation Using a Financial Calculator

Whereas is it useful to know these formulas, calculating present and future values can also be done with the use of a financial calculator. On these calculators, all that is needed to do is input the values for present value, payment amount, interest rate and number of years of the annuity, and then calculate for future value.