Time Value of Money (Annuity)

Future Value of an Annuity
An annuity is a series of equal payments made at fixed intervals for a specified number of periods. If the payments occur at the end of each period, as they typically do, the annuity is called an ordinary or deferred annuity.

Equation 3
FVAn = PMT (FVIFAi,n)
Where
FVAn = The future value of an annuity over n periods
PMT = The payments at the end of each period
FVIFAi,n = Future value interest factor for a annuity

If you deposit $100 at the end of each year for three years in a savings account that pay 5 percent interest per year, how much will you have at the end of three years?

Spreadsheet Solution
In Excel, click the function wizard, Financial, FV, and OK to get the FV dialog box. Then, we would enter 0.05 for Rate, 3 for Nper, and -100 for Pmt (the payment is entered as a negative number to show that it is a cash outflow). We would leave PV blank because there is no initial payment, and we would leave Type blank to signify that payments come at the end of the periods. Then, we clicked OK, we would get the FV of the annuity, $315.25.

If payments are made at the beginning of each period, the annuity is an annuity due.

Equation 4
FVAn (Annuity due) = PMT (FVIFAi,n)(1+i)

For the annuity due, proceed just as for the ordinary annuity except enter 1 for Type to indicate that we now have an annuity due. Then, when you click OK, the answer $331.01 will appear.

Present Value of an Annuity
If the payments come at the end of each year, then the annuity is an ordinary annuity.

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