The present value 
of a single payment made at 
periods in the future is
 |
(1)
|
where 
is the number of periods until payment, 
is the payment amount, and 
is the periodic discount rate. The present value 
of equal payments made each successive period in perpetuity
(a.k.a. the present value of a perpetuity) is given by
 |
(2)
|
The present value 
of equal payments made each successive period for 
periods (a.k.a. the present value of an annuity) is given
by
![v^'=v_infty-v_n=p/r[1-1/((1+r)^n)],](/images/equations/PresentValue/NumberedEquation3.svg) |
(3)
|
where 
is the periodic payment amount.
