Recall, that the present value of an ordinary annuity formula can be used to calculate the present value of a stream of payments received at the end of each year. The formula is as follows:
Compared to an ordinary annuity, the present value of an annuity due can be calculate by modifying the formula above with the addition of the quantity
(1 + r) as follows:
Where:
PMT = payment
r = rate
n = periods
Assume an individual won the lottery and the prize was to be a series of $1,000 payments received at the beginning of each year, over a ten year period. The winner has the option of choosing between the stream of payments or a lump sum discounted at a required rate of 7%, we can calculate what the present value of the stream of payments is as follows:
Using an HP12C calculator, we can solve the equation above using the following keystrokes:
[g][BEG]
[1000][PMT]
[7][i]
[10][n][PV]