TAI "ES 
EXPLANATION OF TABLE 2; 
Annuity WarcE WiLL AMOUNT To ONE DOLLAR IN A GIVEN TIME 
Table 27 shows the annual investment necessary to accumus- 
late $1 in a given number of years at interest rates ranging from 
I to 10 per cent per annum. The annuity is assumed to be 
applied at the end of each year. The table shows in each case 
the sum of the annual installments plus the interest earnings. 
This table is based on the following formula: 
Let a,’ represent the annual installment which at com- 
pound interest in # years will amount to $r. 
Let n represent the number of years required by the annu- 
ity to amount to $1. 
Let 7 represent the interest rate expressed in per cent, as 
0.05 for 5 per cent. 
Then 
/ L 
a, = CHT =a 4) 
and it follows from equation (22) that 
; I 
OG =~. (24a) 
In other words the annuity which will amount to $1 in a given 
time can be found with the aid of a table showing the amount of 
an annuity of $1. It is the reciprocal of the latter. 
Example. — What annuity will amount at 5 per cent compound 
interest to $7500 in 31 years? 
From Table 27 the annuity which will amount to $1 in 31 
years at 5 per cent is found to be 0.014132. The annuity which 
will amount to $7500 in 31 years is, therefore, 
7500 X 0.014132 = $105.99. 
Or from Table 26 the amount of an annuity of $1 for 31 years 
at 5 per cent is found to be $70.76079, therefore, the annuity 
which will amount to $7500 in 31 years will be 
7500 
70.76079 $105.99. 
+ BLL. 377 
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