The Calculation of PWD

Author: E.E. Kimberly

In the following analysis.

The first motor requires an investment of Cc dollars immediately. Thus,

To provide another Cc dollars with which to buy the second motor at the end of n years, it is necessary to invest at interest now the amount

Similarly, to provide money for purchase of the third motor, it is necessary to invest at interest now the amount

Then, the present worth PW₀ of the investment and reinvestment for the life of three machines would be

If it were likely that the service would be required indefinitely, it would be necessary to sum up the preceding series to '(xn+1) terms. However, in dealing with a rapidly progressing science such as the applications of electricity to industry, it is pure folly to assume that obsolescence will not retire any piece of apparatus in less than 100 years.