Present value of an Annuity can be expressed as, where:
A = the annuity received at the end of each year
i = the annual interest or discount rate
PVa = the present value of the future annuity, and
n = the number of years for which the annuity will last
1
\(P V_a=n \displaystyle \sum_{i=1}^A \frac{1}{(1+t)^i}\)
2
\(P V_a=A \displaystyle \sum_{i=1}^n \frac{1}{(1+i)^i}\)
3
\(P V_a=i \displaystyle \sum_{n=1}^A \frac{1}{(1+t)^i}\)
4
\(P V_a=n \displaystyle \sum_{i=1}^n \frac{1}{(1+i)^i}\)