How to Calculate the Present Value of an Ordinary Annuity

The present value of an ordinary annuity formula can be used to calculate the present value of a stream of income payments, the formula is as follows:

Where:
PMT = payment
r = rate
n = periods

Assume you won the lottery and the prize is a $1,000 series of payments to be received over the next ten years, at the end of each year. As the winner you could choose either the $1,000 stream of payments or a lump sum discounted at a required rate of 7%. We can calculate the lump sum as follows:

Give the result above, as long as the lump sum is exactly $7,023.58, and assuming you could realize a 7% return over ten years, you should be indifferent to receiving a lump sum or the stream of payments. If the lump sum offered is less than $7,023.58, you should chose the income; however, if the lump sum offered is greater than $7,023.58 you should choose the lump sum over the payment stream.

Using an HP12C calculator, you can calculate the present value of an ordinary annuity with the variables above using the following keystrokes:

[1000][PMT]
[7][i]
[10][n][PV]