86 VALUATION, DEPRECIATION AND THE RATE-BASE
annum treated as an annuity for the remaining 10 years, which,
at 6 per cent per annum, is $64.17.
At the end of 10 years, the original owner, keeping for his own
use the money in the replacement fund, will be satisfied to sell
at $64.17. The purchaser, content in this case with the assumed
rate of interest of 6 per cent, will be willing to pay $64.17, because
 at the end of the plant’s useful life, he will have recovered
his investment with 6 per cent interest compounded annually.
He will then be under the same necessity of replacing the plant,
making a new investment of $100, as the original owner would
have been if he had remained in possession.
During the entire 20 years of usefulness the plant has been
rendering adequate service. The efficiency of the service is independent
 of, and bears no relation to, the useful life of the plant,
nor to the fact that some or all of its parts were gradually deteriorating.

Interchange of Terms — Depreciation, Amortization and Replacement.
 — It cannot be known just how, nor at what rate,
the actual deterioration of a plant takes place. This may be
rapid at some period of its life, and slow at another, but, as the
plant is supposed, at all times during its life, to be adequately
performing the service expected of it, variations in this rate of
deterioration are immaterial. In other words, the amortization
 of capital is a question which may be considered without
regard to the physical condition of a plant at any period of its
life. Nevertheless many engineers and economists have found
it convenient to consider the actual, or the theoretical accumulation
 in an amortization fund as the measure of plant depreciation
 with a consequent interchange of terms. The term “ depreciation”
 is frequently used when the term amortization”
would be more appropriate.
There is a clear distinction between amortization and replacement.
 The amortization deals with the retirement of the invested
 capital. This may be in installments in uniform or in
unequal annual amounts, or in a lump sum at the end of useful
life. The replacement may mean the substitution of a new