Many times we will find uniform series of receipts or disbursements. Automobile loans, house payments, and many other loans are based on a uniform payment series. It will often be convenient to use tables based on a uniform series of receipts or disbursements.

The series A is definedas follows:

A = An end-of-periodl cash receipt or disbursementin a uniform series, continuing for n periods, the entire series equivalent to P or F at interest rate i

The horizontal line in Figure 4-1 is a representation of time with four interest periods illustrated. Uniform payments A have been placed at the end of each interest period, and there are as many A's as there are interest periods n. (Both these conditions are specifiedin the definitionof A.) Figure 4-1 uses January 1 and December 31, but other 1-year periods could be used.

We will use this relationship in our uniform series derivation.
Figure 4-1  The general relationship between A and F.

1 In textbooks on economic analysis, it is customary to define A as an end-of-period event rather than a.
beginning-of-period or, possibly, middle-of-period event. The derivations that follow are based on this
end-of-period assumption. One could, of course, derive other equations based on beginning-of-period
or mid period assumptions.

Looking at Figure 4-1,we see that if an amount A is investedat the end of each year for 4 years, the total amount F at the end of 4 years will be the sum of the compound amounts of the individual investments.

In the general case for n years,

Multiplying Equation (4-1) by (1 + i), we have .

Factoring out A and subtracting Equation 4-1 gives

Solving Equation 4-4 for F gives

Thus we have an equation for F when A is known. The term inside the brackets 

is called the uniformseries compound amount factor and has the notation (F/A, i,n).


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