Perpetuities and Annuities

A perpetuity is an infinite sequence of payments. If someone offered to pay you $100 per year from now until the end of the world, that would be a perpetuity. An annuity is a finite sequence of payments. If someone offered to pay you $100 per year for the next ten years, that would be an annuity. Perpetuities and annuities are commonly encountered in time value of money calculations. A series of coupon payments on a bond and monthly payments on a 30-year mortgage are examples of annuities.

The following formula is used to calculate the present value of a perpetuity that starts one year from the present date:

PV =  CF 
r

where CF is the annual cashflow amount and r is the discount rate.

The following formula is used to calculate the present value of an annuity that lasts n years and starts one year from the present date:

PV = CF * (  1 
r
-      1     
r * (1 + r)n
)