300 VALUATION, DEPRECIATION AND THE RATE-BASE 
EXPLANATION OF TABLE 23 
Tae PRESENT VALUE OF AN ANNUITY OF ONE DOLLAR 
The present value of an annuity is the sum of the present values 
of the several annuity installments. 
The present value of an annuity of $1 receivable at the end 
of each year is presented for a few selected years in Table 28. 
This table is based on the following formula: 
Let P’ represent the present value of an annuity of $1 re- 
ceivable at the end of each year during # years. 
Let # represent any number of years, the term of the 
annuity. 
Let ¢ represent the rate of interest expressed decimally; 
thus for 5 per cent, ¢ = 0.05. 
Then: 
bs x a cn 1 ms Lil nf 
Bir mry S] (: G+ 5) GC 
This equation may be written: 
+9)" —1 I 
1 mn ee eer _— reo 
l= eh (=) 
Or by reference to equations (19) and (22) 
AY 
P = ov iil =) 
In other words the present value of the annuity of $1 is the 
amount of an annuity of $1 in # years divided by the amount 
of $1 at compound interest in 7 years. 
The present value of an annuity of $1 receivable at the end 
of each year is therefore ascertainable for any number of years 
to 100 from Tables 22 and 26 by dividing the amount of an 
annuity of $1 found in Table 26 by the amount of $1 at com- 
pound interest found in Table 22. 
Example. — What is the present value of an annuity of $53 
receivable at the end of each year for 20 years at 5 per cent 
interest? 
6) 
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