Future Value of Uniform Annual Series

The Equation 3.2a for the future value of a uniform annual series of A is the transposition of equation 2.3a.

The cash flow diagram corresponding to the above equation is

Page 41

Fig. 3.1

Note that Fig. 3.1 is the reverse of Fig. 2.1 in that it brings the annual values forward. The corresponding expression is FV A (F/A. i. n> (3 2 b)

The multiplier (F/A,i,n) is called the sinking fund factor, i.e., $A is sunk every year with interest rate i to receive a future value (FV) n years later.

Please note that for the formula 3.2a and the expression 3.2b to be applicable we must have a value for cost or benefit (even if this value is zero) at the last year, that is year n.

Example 3.2

If we save $500 every year in a bank account that gives 6% interest, how much do we have at the end of the fifth year?

The spreadsheet calculation of the net future worth is shown below. As in the case of the present worth, both expressions to be used from Quattro Pro and Excel are shown. The small difference between the numbers is due to different rounding of the result depending on the number of decimal point.

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