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Interest formulas are used to simplify equivalence calculations for cash flows that involve cash flows that are more complex than a single-period or a few single-period cash transactions. Different interest formulas are used for different cash flow types. All cash flows can be classified as belonging to one of the following five cash flow types: single, uniform series, linear gradient series, geometric gradient series, and irregular series cash flow. Figure 4.8 on page 116 of the text depicts these five different cash flows. Many of the examples from the text discussed previously have made use of a single or a single-period cash flow. Equivalence calculations for such cases are accomplished by the simple use of the compound interest formula. Other cash flow types require additional formulas for equivalence computation. A uniform series cash flow involves a series of equal cash flows at regular intervals. The constant amount of the cash flows in the series is denoted by the symbol A, defined previously. A linear gradient series cash flow is one in which the periodic transactions are increasing or decreasing by a constant amount between each successive time period. When the increase or decrease between adjacent time periods is by a fixed rate, expressed as a percentage, we get a geometric gradient series. Finally, all other cash flow types that can not be classified as one of the four types described above are collectively known as irregular series cash flows. But even though the cash flow for the entire project period may be irregular it is possible that cash flows for shorter duration can be classified as one of the four regular types. Interest tables and factor notation are two tools that can simplify equivalence calculations. Interest tables list factors that are used to convert a known cash flow at some period to an unknown cash flow at a different period, given the interest rate and the number of interest periods between the known and the unknown cash flows. Interest tables use factor notation to list the interest factors. In the example shown at the top of page 119 in the text, the factor needed to convert the present amount ($20,000) to a future amount at the end of period 15 with an interest rate of 12% is 5.4736, expressed at the four-decimal-place accuracy. This factor can either be calculated using the compound interest formula or looked-up in the table on page 891 of the text. The factor can be found in column 1 under single payment, compound amount factor for N = 15 periods. The notational convention used to denote this factor, (F/P, i, N), indicates that we are trying to compute the future worth F, of a present amount P, with an interest rate of i% per period for N periods. In this particular case, P is $20,000, i is 12%, and N is 15 periods. When the present amount is multiplied by this factor we end up with the future worth at the end of 15 periods. |