Interest compound factors

If money is borrowed, interest must be paid over the time period if money is loaned out, interest income is expected to accumulate. In other words, there is a time value associated with the money. Before money flows from different years can be combined, a compound interest factor must be employed to translate all of the flows to a common present time. The present is arbitrarily assumed often it is either the beginning of the venture or start of production. If future flows are translated backward toward the present, the discount factor is of the form (1 + i) , where i is the annual discount rate in decimal form (10% = 0.10) and n is the number of years involved in the translation. If past flows are translated in a forward direction, a factor of the same form is used, except that the exponent is positive. Discounting of the cash flows gives equivalent flows at a common time point and provides for the cost of capital. 

Table 9-3 gives examples of compound-interest factors and example compound-interest calculations. 

Compound Interest Factors 6% Compound Interest Factors ... 

Discrete compound-interest factor (1 + i)H at various values of i and rtf... 

Future worth = present worth x compound interest factor S = pc or... 

As indicated in the footnote for Eq. (12), the common interest expressions can be written in simplified form by using discount-factor and compound-interest-factor notation. Following is a summary showing the significance and meaning of the compounding factors presented in Table 3, Derivations of the factors are presented in the text. 

C = compound interest factor CR = cost for replacement or other asset, dollars Cv = original cost of equipment or other asset, dollars d = number of days in an interest period, days, or derivative e = base of the natural logarithm = 2.71828... ... 

Compound interest factors definition of 223n., 236-237 tables of 219, 234-235, 240-246 (See also specific name)... 

In an economic evaluation of a project, it is often necessary to evaluate the present value of funds that will be received at some definite time in the future. The present value (PV) of a future amount can be considered as the present principal at a given rate and compounded to give the actual amount received at a future date. The relationship between the indicated future amount and the present value is determined by a discount factor. Discounting evaluates each year s flow on an equal basis. It does this by means of the discount, or present value factor, and the reciprocal of the compound interest factor (1 -(- i)" with... 

Compound Interest Factors Discrete Cash Flow, Discrete Compounding 2.4.1. Compound Amount Factor (Single Payment)... 

Compound Interest Factors Continuous Uniform Cash Rows, Continuous... 

Compound Interest Factors Discrete Cash Flow, Discrete Compounding... 

The compound interest factors described in this section are used for discrete cash flows compounded discretely at the end of each interest period. AH of these factors can be found in Table 1, including algebraic and functional formats and the Excel functions. The numerical values for each factor for selected interest rates can be found in the tables at the end of this chapter. Complete tables can be found in the Additional Reading at the end of the chapter. The notation used in this chapter is... 

Many times annual payments do not occur in equal amounts. Inflation causes annual increases in operating costs, and maintenance costs often increase with the age of the equipment. If a series of payments increases by an equal amount or gradient, G, each year, then a special compound interest factor can be used to reduce the gradient series to an equivalent equal-payment series. The following illustration shows a four-period gradient series that increases by G each period. 

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