iemisc (version 0.9.9)

PgivenA1: Present value for geometric gradient series (Engineering Economics)

Description

Compute P given A1

Usage

PgivenA1(A1, i, f, n)

Value

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

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

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

or

$$P = A_1n\left(1 + i\right)^{-1}, \: where \: f = i$$

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"

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

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%