In common terms the present value of a regular annuity may be shown as given below:
PVNn = A/(1 + k) + A/(1 + k)^{2}+ ..................+ A/(1 + k)^{N}
= A (1/(1 + k) + 1/(1 + k)^{2}+ ..................+ 1/(1 + k)^{N})
= A [((1 + k)^{N}- 1)/(k (1 + k)^{n})]
In case of annuity due:
PVA_{n (due )} = A [(1 + k)n - 1)/(k (1 + k)^{n})] (1 + k) ...........................Eq(12)
Here PVA_{n} = Present value of an annuity that has a duration of n periods;
A = Constant periodic flows and k = discount rate