## Present Value of Arithmetic Gradient Series

These are annual series with constant increasing values such that

The cash flow diagram is shown in Fig. 2.2, and G is called the gradient.

The present value is r = a

As in the other expressions, the value of (P/G, i, n) can be found in the compound interest tables. Example 2.2

A project has a net income of \$50 the first year, increasing by \$100 every year for the next three years. What is the net present worth of this project at an interest rate of 10%?

In this example, the annual income is determined according to an arithmetic series, and we have to apply equation 2.4a or expression 2.4b.

The following cash flow diagram presents the model for this example.

The above cash flow can be broken into two cash flows as in Fig. 2.4b and the calculation is

Fig. 2.4b

The spreadsheet calculation is shown below. As can be seen we used the same spreadsheet configuration in this case as for Example 1.2. In using the compound interest table, we had to break the cash flow diagram into two components and use the P/G and P/A expressions. The use of the spreadsheet made the operation a lot simpler.

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