Single-Amount Factors (F / P and P / F)
The most fundamental factor in engineering economy is the one that determines the amount of money F accumulated after n years (or periods) from a single present worth P, with interest compounded one time per year (or period). Recall that compound interest refers to interest paid on top of interest. Therefore, if an amount P is invested at time t = 0, the amount F1 accumulated 1 year hence at an interest rate of i percent per year will be
where the interest rate is expressed in decimal form. At the end of the second year, the amount accumulated F2 is the amount after year 1 plus the interest from the end of year 1 to the end of year 2 on the entire F1
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| Figure 2–1 Cash fl ow diagrams for single-payment factors: (a) fi nd F, given P, and (b) fi nd P, given F. |
A standard notation has been adopted for all factors. The notation includes two cash fl ow symbols, the interest rate, and the number of periods. It is always in the general form (X /Y, i, n ). The letter X represents what is sought, while the letter Y represents what is given. For example, F /P means fi nd F when given P. The i is the interest rate in percent, and n represents the number of periods involved.
Using this notation, (F/P ,6%,20) represents the factor that is used to calculate the future amount F accumulated in 20 periods if the interest rate is 6% per period. The P is given. The standard notation, simpler to use than formulas and factor names, will be used hereafter.
Table 2–1 summarizes the standard notation and equations for the F/P and P/F factors. This information is also included inside the front cover.
To simplify routine engineering economy calculations, tables of factor values have been prepared for interest rates from 0.25% to 50% and time periods from 1 to large n values, depending on the i value. These tables, found at the rear of the book, have a colored edge for easy identifi cation. They are arranged with factors across the top and the number of periods n down the left side.
The word discrete in the title of each table emphasizes that these tables utilize the end-of-period convention and that interest is compounded once each interest period. For a given factor, interest rate, and time, the correct factor value is found at the intersection of the factor name and n . For example, the value of the factor (P/F,5%,10) is found in the P/F column of Table 10 at period 10 as 0.6139. This value is determined by using Equation [2.3].
For spreadsheets, a future value F is calculated by the FV function using the format
A present amount P is determined using the PV function with the format
These functions are included in Table 2–1. Refer to Appendix A or Excel online help for more information on the use of FV and PV functions.
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3 comments:
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