# PgivenA1: Present value for geometric gradient series (Engineering... In iemisc: Irucka Embry's Miscellaneous Functions

## Description

Compute P given A1

## Usage

 1 PgivenA1(A1, i, f, n) 

## Arguments

 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)

## Details

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"

## Value

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

## References

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.

## Examples

 1 2 3 4 5 6 7 library("iemisc") # Example 4-23 from the Reference text (page 158-159) PgivenA1(1000, 25, 20, 4) # i is 25% and f is 20% # Example 4-24 from the Reference text (page 159) PgivenA1(1000, 25, -20, 4) # i is 25% and f is -20% 

iemisc documentation built on Aug. 2, 2020, 9:07 a.m.