## Annuity and Annuity Due

An **annuity** is a stream of payments made through time. A stream of equal payments at equal time intervals is a **fixed annuity**. If those payments are made at the end of each time period (month, quarter, year, etc…) it is an **Ordinary Annuity**. If the payments are due at the beginning of each period, it is an **Annuity Due**. We can convert the valuation of an **ordinary annuity** to an **annuity due** by compounding the resulting future value for one more period. (Since the payments for an annuity due are all due at the beginning of the period, instead of the end like with an ordinary annuity, this makes it effectively one period sooner, but not one more payment.)

The payment amount, interest rate, and number of payments all contribute to the future value of the annuity. Any annuity calculation has these four variables, and with any three you can find the fourth.

The formula in the following section and Formula Solver! series example further below calculates the future value of an ordinary annuity from the interest rate, payment amount, and number of payments (periods) and then compounds for one more period to calculate the future value of an annuity due.

## Formula for Future Value of Annuity Due

To Calculate the Future Value of an Annuity Due FV(AD), we first treat it as an ordinary annuity, and then compound that value for one more period. The Future Value of an Ordinary Annuity FV(OA) formula is:

**FV(OA) = PMT · [((1 + i) ^{n} – 1) / i ] **where:

- PMT = periodic payment

i = periodic interest rate (annual rate divided by number of periods per year)

n = number of periods (or number of payments)

This resulting FV(OA) is compounded one more time to convert to Future Value of an Annuity Due:

**FV(AD) = FV(OA) • (1 + i) **

## Future Value of an Annuity Due

Calculate the Future Value of an Annuity Due with a step by step example using your values for the periodic interest rate, number of periods, and periodic payment amount.