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