304 VALUATION, DEPRECIATION AND THE RATE-BASE 
EXPLANATION OF TABLE 26 
Tae AMOUNT OF AN ANNUITY OF ONE DOLLAR 
An annuity is a sum uniform in amount due annually. 
The amount of an annuity in any term or number of years is 
the sum of the several annual installments with interest thereon 
during the term compounded annually. 
Table 26 shows the amount of an annuity of one dollar paid 
at the end of each year with the earned interest increments of 
each year added at the end of the year. 
To find the amount of an annuity of $1 paid at the beginning 
of each year subtract $1 from the figures noted in the table and 
the result will then apply at the beginning of each year, or, which 
is the same, at the end of the preceding year. Thus for 6 per 
cent interest at the beginning of the year 1, the amount is zero; 
at the end of year 11, or beginning of the year 12, it is $16.37 — 
1.00 = $15.37. 
The values given in Table 26 are calculated by the following 
formula: 
Let A” represent the amount of an annuity of $1 paid at the 
end of each year. 
Let i represent the interest rate expressed in percentage, as 
o.os for 5 per cent. 
Let # represent the number of years. 
Then 
A (rhiiy — 3 (2+) 
7 
and it follows from equation (19) that: 
! 
Al = 4 (22a) 
The amount of an annuity of $1 paid at the end of each year 
can be found, in other words, from any table giving the amount 
of $1 at compound interest by subtracting $1 from the amount 
found in the compound interest table and dividing the remainder 
by the rate of interest expressed decimally. 
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