### Compute the Present Value, Knowing the Arithmetic Gradient of Maintence Cost.

Assume the maintenance costs occur at the end of each year and that the bank pays 5% interest. How much should the car owner deposit in the bank now?

**SOLUTION**The cash flow may be broken into its two components:

Both components represent cash flOws for which compound interest factors have been derived. The

first is a uniform series present worth, and the second is an arithmetic gradient series present worth:

**P = A(P / A, 5%, 5) + G(P / G, 5%,5)**

Note that the value of n in the gradient factor is 5, not 4. In deriving the gradient factor, we had (n - 1) terms containing G. Here there are four terms containing G.

Thus, (n - 1) = 4, so n = 5.

He Should deposit $766 in the bank now.

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