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

A man has purchased a new automobile. He wishes to set aside enough money in a bank account to pay the maintenance on the car for the first 5 years.It has been estimated that the maintenance cost of an automobile is as follows:

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.