# Present value of a deferred annuity

## Input(s)

\(i_{e}\): Effective Interest or Discount Rate (fraction)

\(\mathrm{t}:\) Time (year)

\(A_{v}\): Annuity (currency unit)

## Output(s)

\(P_{v}\): Present Value of Deferred (currency unit)

## Formula(s)

\[
P_{v}=A_{v} * \frac{\left(\left(1+i_{e}\right)^{t}\right)-1}{i_{e} *\left(1+i_{e}\right)^{t}} *\left(\frac{1}{\left(1+i_{e}\right)^{t-2}}\right)
\]

## Reference(s)

Mian, M. A. 2011. Project Economics and Decision Analysis Volume 1: Deterministic Models, Second Edition. Tulsa, Oklahoma: PennWell Corporation. Chapter 2, Page: 62.