Present value of a perpetuity, Financial Accounting

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PVA_∞ = A(1 + k)^-1 + A(1 + k)^-2+..... + A(1 + k⁾^∞^{+ 1}+ A (1 + k)_∞

Multiplying both the sides of Eq (a7) by (1+k) provides:

PVA_∞ = (1 +k) = A(1 +k) +A (1 +k)^-1 +......A (1 +k)^-∞⁺² +A(1 + k)^-∞⁺¹

Subtracting Eq (a7) from eq (a8) provides:

PVA_∞ k = A [1 - (1 + k)^∞]

As (1 + k)^-∞ → o eq.(a8) turns into:

PVA_∞ k = A

⇒ PVA_∞ = A/k

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