## 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)