ACTUAL AND PROBABLE LIFE :
enth, 8oo at the end of the twelfth, and so on to the last 100 at
the end of the nineteenth.
By substituting dollars for articles and computing the annuity
at 6 per cent interest required for the replacements of each year
it will be found that an annuity of $94 will be required to
replace the failures of the first year, an annuity of $97 to re-
place those of the second year, an annuity of $94 to replace
those of the third year, an annuity of $91 to replace those of
the fourth year, and so on to the nineteenth year. The sum of
these annuities is $1101 or 11.01 per cent.
If the articles which fail each year are replaced and the re-
quired annuities for these replacements are also taken into
account then the sum of the annuities at 6 per cent interest will
be: 11.01 per cent the first year, 10.17 per cent the second, 9.41
per cent the third, 8.78 per cent the fourth, 8.26 per cent the fifth,
7-86 per cent the sixth and so on to a minimum in about the
fourteenth year of a little over 7 per cent, and thereafter grad-
ually increasing to about 11 per cent in the thirtieth year.
Had the determination been made in the usual way, based on
the assumption that no distinction need be made between the
actual and the probable life, the allowance for replacements
would have been 7.59 per year, continuously from the beginning.
Conceding a moderate or even a wide range of error due to an
almost arbitrary though reasonable assumption of the probable
annual failures when average life is known, the result of the
computation of what should be set aside annually on the annuity
basis, to meet the replacements, when compared with the an-
nuity determined from probable life new, shows that the latter
is insufficient.
The computation also shows that the required earnings based
on this determination would be undesirably high at the begin-
ning, in the early years, when they should be low.
No further demonstration than the above will be needed to
show the futility of depending on the Sinking Fund Method
and the Equal Annual Payment Method as usually applied,
when estimating the replacement requirements.
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