### Geometric Gradient Series Factors

A geometric gradient series is a cash flow series that either increases or decreases by a constant percentage each period. The uniform change is called the rate of change

Note that the initial cash flow A1 is not considered separately when working with geometric gradients.

**Figure 2–21**shows increasing and decreasing geometric gradients starting at an amount A1 in time period 1 with present worth Pg located at time 0. The relation to determine the total present worth Pg for the entire cash flow series may be derived by multiplying each cash flow in

**Figure 2–21**a by the

Figure 2–21 Cash flow diagram of (a) increasing and (b) decreasing geometric gradient series and present worth Pg. |

The (P A,g,i,n) factor calculates Pg in period t = 0 for a geometric gradient series starting in period 1 in the amount A1 and increasing by a constant rate of g each period.

The equation for Pg and the ( P/A , g , i , n ) factor formula are

It is possible to derive factors for the equivalent A and F values; however, it is easier to determine

the Pg amount and then multiply by the A/P or F/P factor.

the Pg amount and then multiply by the A/P or F/P factor.

As with the arithmetic gradient series, there are no direct spreadsheet functions for geometric gradient series. Once the cash flows are entered, P and A are determined using the NPV and PMT functions, respectively.

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