**What Is an Annuity?**

An annuity is a series of equal payments made at equal intervals. Annuity payments don’t have to be made annually but can be made monthly, weekly, or even daily.

The critical factors are:

- The payments equal each other and;
- The interval between the payments is the same.

**Annuity Due** is the one in which payments are made at the beginning of each period.

**Formula **

More generally, for any size of payment and number of time periods, the future value of an annuity due is equal to

\[\begin{matrix}F{{V}_{\text{annuity due}}}=PMT\times \frac{{{\left( 1+i \right)}^{n}}-1}{i}\times \left( 1+i \right) & \left( 1 \right) \\\end{matrix}\]

Where

PMT=the periodic payment in the annuity

i=the interest rate

n= the number of payments

**Example 1** FV of an Ordinary Annuity and an Annuity Due

You have been provided an investment chance that will pay you $5,000 per year for next 6 years. What is the value of this stream of cash flows at the end of year 6 if you get payments at the end of each year and you expect a return of 7%? What if you obtain payments at the beginning of each year?

**Solution**

In this example,

\[\begin{align}& PMT=5,000 \\& i=0.07 \\& n=6 \\\end{align}\]

For the ordinary annuity timing, the solution is

\[\begin{align}& F{{V}_{\text{ordinary annuity}}}=PMT\times \frac{{{\left( 1+i \right)}^{n}}-1}{i} \\& =\$5,000\times\frac{{{\left(1.07\right)}^{6}}-1}{0.07}=\$35,766.45\\\end{align}\]

For the annuity due timing, the solution is

\[\begin{align}& F{{V}_{\text{annuity due}}}=PMT\times \frac{{{\left( 1+i \right)}^{n}}-1}{i}\times \left( 1+i \right) \\& =\$5,000\times\frac{{{\left(1.07\right)}^{6}}-1}{0.07}\times\left(1.07\right)=\$38,270.11\\\end{align}\]