Description Usage Arguments Details Value References Examples

Compute P given A1

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`A1` |
numeric vector that contains the initial annual value(s) |

`i` |
numeric vector that contains the interest rate(s) as a percent |

`f` |
numeric vector that contains the average interest rate value(s) as a percent per period |

`n` |
numeric vector that contains the period value(s) |

P is expressed as

*P = \frac{A_1≤ft[1 - ≤ft(1 + i\right)^{-n}≤ft(1 + f\right)^{n}\right]}{i - f}, \: where \: f \neq i*

or

*P = A_1n≤ft(1 + i\right)^{-1}, \: where \: f = i*

*P*"the present equivalent of the geometric gradient series"

*A_1*"the initial cash flow in that occurs at the end of period one"

*i*the "interest rate per period"

*f*the "average rate each period"

*n*the "number of interest periods"

Note: "f can be positive or negative"

PgivenA1 numeric vector that contains the present value(s) rounded to 2 decimal places

William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling, *Engineering Economy*, Fourteenth Edition, Upper Saddle River, New Jersey: Pearson/Prentice Hall, 2009, page 156-159.

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