42 ME M O IR S of the 
is to be noted, that the firll term of all thefe proportions is the 
lame throughout ^ viz. N n r, the lecond changing yearly accord- 
ing to the decreafe of R, r, f, and encreafe of 1, y, vj and the 
third are fucceffively the prefent value of money payable after 
one, two, three, ^c. years, according to therateof intereft agreed 
on 5 thele numbers, being in all cafes of neceflary ule, are put 
into the following table, and they are the decimal values of one 
pound payable after the number of years in the margin, at the 
rate of 6 per Cent, 
1 ears 
Prelcnt va- 
Years 
Prefent va- 
Years 
Prelent va- 
lue of I /. 
lue of I /. 
lue of I /. 
I 
0,9434 
19 
0,3305 
37 
0,1158 
2 
0,8900 
20 
0,3118 < 
38 
0,1092 
0,8396 
21 
0,2941 
39 
0,1031 
4 
0,7921 
22 
0,2775 
40 
0,0972 
5 
0,7473 
^3 
0,26-18 
45 
0,072(7 
6 
0,705c 
24 
0,2470 
50 
0,0543 
7 
0,6650 
25 
0,2330 
55 
0,0406 
8 
0,6274 
26 
0,2198 
60 
0,0303 
9 
0,5919 
27 
0,2074 
^5 
0,0227 
'lO 
0,5584 
28 
0,1956 
70 
0,0169 
II 
0,5268 
29 
0,1845 
75 
o,oi2<:> 
ii 
c,4970 
30 
0,1741 
80 
0,0094 
13 
0,4688 
31 
0,1643 
85 
0,0071 
14 
0,4423 
32. 
0,1550 
90 
0,0053 
15 
0,4173 
33 
0, 146-2 
95 
0,0039 
16 
0,3936 
34 
0,1379 
ICO 
0j0C25> 
17 
o,37U 
35 
0,1501 
18 
0,^50? 
36 
0,1227 
It were needlels to advertile that the great trouble of working 
fo many proportions will be vefy much alleviated by ufing loga- 
rithms 5 and thar inftead of employing 'Snv — Yji; for the le- 
cond term of the proportion in finding the value of three lives, it 
may fufficeto ufe only Yyv^ and then dedu6^ing the fourth term 
io found out of the third, the remainder v;ill be the prefent value 
ibught^ or all thele fourth terms being added together, and de- 
du6tcd out of the value oFthe certain annuity for lo m.any years, 
will leave the value of the contingent annuity upon the chance of 
mortality of all thofe three lives 5 for example, let there be 3 
lives of 10, 30, and 40 years of age propofed, and the proper- 
fions will be thus : 
As 
