2.6 - Geometric Gradients

In the previous section, the procedure for handling cash flows which change by a constant amount from one interest period to the next (i.e. arithmetic gradients) was introduced. In this section, cash flows which change by a constant percentage from one interest period to the next (i.e. geometric gradients) are discussed. The equation for calculating the present worth of a geometric gradient is:

For a decreasing gradient, change the sign in front of both g's in the present worth equation.
When g = i, the present worth of a geometric gradient series is:

P= An/(1+i)


The following example illustrates the procedure.

Example 2.8 - Increasing Geometric Gradient

A mechanical contractor is trying to calculate the present worth of personnel salaries over the next five years. He has four employees whose combined salaries thru the end of this year are $150,000. If he expects to give each employee a raise of 5% each year, the present worth of his employees' salaries at an interest rate of 12% per year is nearest to:

(A) $591,000  (B) $816,100  (C) $702,900  (D) $429,300
Solution:

The cash flow at the end of year 1 is $150,000,
increasing by g=5% per year.  Therefore,
the present worth is:


Answer is (A)

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