## Compound Interest Factors for Discrete Compounding

Compound interest factors are formulas that define mathematical equivalence for specific common cash flow patterns. The compound interest factors permit cash flow-analysis to be done more conveniently because tables or spreadsheet functions can be used instead of complicated formulas. This section presents compound interest factors for four discrete cash flow- patterns that are commonly used to model the timing of receipts and disbursements in engineering economic analysis. The four patterns are:

1. A single disbursement or receipt

2. A set of equal disbursements or receipts over a sequence of periods, referred to as an annuity

CHAPTER 3 Cash Flow Analysis

3. A set of disbursements or receipts that change by a constant amount from one period to the next in a sequence of periods, referred to as an arithmetic gradient series

4. A set of disbursements or receipts that change by a constant proportion from one period to the next in a sequence of periods, referred to as a geometric gradient series

The principle of discrete compounding requires several assumptions:

1. Compounding periods are of equal length.

2. Each disbursement and receipt occurs at the end of a period. A payment at time 0 can be considered to occur at the end of period — 1.

3. Annuities and gradients coincide with the ends of sequential periods. (Section 3.8 suggests several methods for dealing with annuities and gradients that do not coincide with the ends of sequential periods.)

Mathematical derivations of six of the compound interest factors are given in Appendix 3 B at the end of this chapter.

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