38 
MEMOIRSe/^/iJ^ 
of infuring the life of a man 6f 2a and 50 is difcovered 5 for in- 
ftance, it is 100 to i, that a man of 20 dies not in a year, 
and but 98 to i for a man of 50 years of age. 
Ufe fifth, on this depends the valuation of annuities upon 
lives y for it is plain that the piirchafer ought to pay for only iuch 
a part of the value of the annuity, as he has chances that he is 
living 'y and this ought to be computed yearly, and the fum of all 
thofe yearly values, being added together, will amount to the 
value of the annuity for the life of the perfon propoled 5 now 
the preient value of money payable after a term of years, at any 
given rate of intereft, may be had either from tables already 
computed, or almoft as compendioufly, by the table of loga- 
rithms 3 for the arithmetical Complement of the logarithm of 
unity and its yearly intereft (that is, of i, 06, at 5 per Cent. 
being 9. 97455^4) being multiplied by the number of years pro- 
pofed, gives the prefent value of one pound payable at the end 
of i^o many years 5 then by the foregoing propofition, it will be 
as the number of peribns living after that term of years, to the 
number dead, fo are the odds that any one perlbn is alive or 
dead 5 and confequently,^ as the fum of both, or the number of 
perfons living of the age firft propofed, to the number remaining 
after fo many years (both given by the table ) fo the prefent value 
of the yearly fum payable after the term propofed, to the fum 
which ought to be paid for the chance the perlbn has to enjoy 
fuch an annuity after fo many years 5 and this being repeated for 
every year of the perfon's life, the fum of all the preient values 
of thofe chances is the true value of the annuity 5 and the follow- 
ing table Ihews the value of annuities for every fifth year of age 
to the 70th. 
Age 
dear's Pur. 
Age 
Year's Pur. 
Age 
lear's Pur 
I 
10,28 
25 
12,27 
50 
9,21 
5 
19,40 
30 
11,72 
55 
8,51 
10 
I3'44 
35 
1I;I2 
60 
7,«5'o 
15 
13^33 
40 
10,57 
65 
<^.54 
20 
12,78 
45 
9^9^ 
10 
5.32 
Ufe fixth, two lives are likewife to be valued by the fame 
rule 5 for the number of chances of each fingle life, found in the 
table, being multiplied together, become the chances of the two 
lives 5 and after any certain term of years, the produ£l of the two 
remaining lums is the chances that both the pcrions are living 5 
die produ61: of the two differences, being the numbers of the 
dead 
