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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:
PVAn (due ) = A [(1 + k)n - 1)/(k (1 + k)n)] (1 + k) ...........................Eq(12)
Here PVAn = Present value of an annuity that has a duration of n periods;
A = Constant periodic flows and k = discount rate
Equation illustrates the relationship in between PVA n , A, K and n. So manipulating this a bit: We find that A = PVA n [(k (1 + k) n )/((1 +k) n - 1)] [(k (1 + k) n )/(
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