T+ "ES 
EXPLANATION OF TABLE 25 
THE PRESENT VALUE OF ONE DorrAarR DUE AT A FUTURE DATE 
The present value of $1 due at some future time is the sum 
which placed at compound interest will amount to $1 at that 
time. 
The formula on which Table 25 is based is as follows: 
Let P represent the present value of $1 due at the end 
of n years. 
Let n represent any number of years. 
Let 7 represent the interest rate expressed decimally as 0.05 
for 5 per cent. 
I 
Then P = (x +3)" (20) 
Table 235 has been prepared for only a few selected years because 
the present value of $1 due at a future time is also readily obtain- 
able from Table 22. According to equation (19), A’ may be 
substituted for (1 + ¢)”, equation (20) may then be written: 
I 
P= VL (21) 
That is to say, the present value of $1 due at any future time is 
the reciprocal of $1 at compound interest for the same time. 
Example. — What is the present value of $600 due in 8 years 
at 4 per cent interest? 
From Table 22 the amount of $1 at 4 per cent compound 
interest in 8 years is $1.368569, consequently the present value 
of $1 due in 8 years will be 
I + 1.368560 = 0.730690 
and the present value of $600 due in 8 years at 4 per cent will be 
0.730690 X 600 = $438.41. 
Note. — To find the present value of $1 due at the end of 
any number of years # not noted in this table, select two or 
. ABIL. 
351