Editing Present value (section)

====Present value of a perpetuity====
A [[perpetuity]] refers to periodic payments, receivable indefinitely, although few such instruments exist. The present value of a perpetuity can be calculated by taking the limit of the above formula as ''n'' approaches infinity.

:<math>PV\,=\,\frac{C}{i}. \qquad (2)</math>

Formula (2) can also be found by subtracting from (1) the present value of a perpetuity delayed n periods, or directly by summing the present value of the payments

:<math>PV = \sum_{k=1}^\infty \frac{C}{(1+i)^{k}} = \frac{C}{i}, \qquad i > 0,</math>

which form a [[geometric series]].

Again there is a distinction between a perpetuity immediate – when payments received at the end of the period – and a perpetuity due – payment received at the beginning of a period. And similarly to annuity calculations, a perpetuity due and a perpetuity immediate differ by a factor of <math>(1+i) </math>:

:<math> PV_\text{perpetuity due} = PV_\text{perpetuity immediate}(1+i) \,\!</math><ref name="Broverman"/>