044 
LIFE-ANNUITY. 
Table IT. Showing the Value of an Annuity on One Life, or Number of Years Annuity in the Value, fuppofing Money to leaf 
Intercf at the feveral Rates of 5, 4, and 5, per Cent. 
Age. 
Years Value at 
3 per-Cent. 
Years Value at 
4 per Cent. 
Years Value at 
5 per Cent. 
Age. 
Years Value at 
3 per Cent. 
:Years Value at 
4 per Cent. 
Years Value 
5 per Cent. 
6 
i8-S 
l6‘2 
I4’I 
41 
130 
II ’4 
I0’2 
7 
i8‘9 
i 6‘3 
14*2 
4 2 
128 
11*2 
10*1 
8 
i9'o 
16-4 
I 4‘3 
43 
I2’6 
III 
100 
9 
i9'o 
16-4 
I 4'3 
44 
I2 '5 
i ro 
9'9 
10 
i9'o 
i 6’4 
i 4'3 
45 
12-3 
xo - 8 
9-8 
11 
19*0 
i6'4 
i 4'3 
46 
12*1 
1 0*7 
9'7 
12 
i8 - 9 
16 '3 
I 4’2 
47 
1 r 9 
i °'5 
9’5 
13 
18-7 
16’ 2 
14- 1 
48 
H-8 
xo'4 
9'4 
14 
i 8'5 
x6’o 
I4'0 
49 
11 *6 
I O' 2 
9'3 
15 
i 8- 3 
1 5 ' 8 
J 3'9 
5 ° 
11*4 
IO'I 
9'2 
l6 
iB'i 
i 5 '6 
i 3-7 
S l 
I 1*2 
9’9 
9-0 
*7 
1 7'9 
J 5'4 
i 3'5 
5 2 
no 
98 
89 
18 
17'6 
i 5 ‘ 2 
J 3'4 
53 
107 
9 '6 
8-8 
i 9 
17-4 
15-0 
lyz 
54 
xo-5 
9'4 
8-6 
20 
I 7’2 
I 4'8 
13-0 
55 
103 
9'3 
8 5 
21 
17*0 
r 4'7 
I 2’9 
5 6 
10 1 
91 
8-4 
22 
i6’8 
I 4’5 
12-7 
5 7 
9'9 
89 
8 • 2 
23 
165 
14-3 
I 2-6 
5 8 
9 '6 
87 
8-i 
24 
163 
14-1 
I2‘4 
59 
9'4 
86 
8'o 
25 
i6*i 
i4’o 
123 
60 
9 ' 2 
8' 4 
79 
26 
15-9 
I 3 ' 8 
I 2 ’ I 
6l 
8.9 
8 ’2 
7'7 
27 
i 5 -6 
13-6 
I 2*0 
62 
8-7 
8-i 
7 6 
28 
1 5'4 
J 3‘4 
xi-8 
63 
8 '5 
7'9 
7'4 
29 
J 5 ' 2 
13 " 2 
1 1'7 
64 
8 3 
7.7 
7-3 
30 
I 5 '° 
131 
11 *6 
65 
8-o 
7‘5 
7 'i 
3 1 
14-8 
129 
ii -4 
66 
7 s 
7-3 
6'9 
3 2 
i4'6 
127 
113 
67 
7*6 
71 
67 
33 
14-4 
1 z '6 
11*2 
68 
714 
6-9 
6-6 
34 
14*2 
I 2’4 
I 1*0 
69 
7 'i 
67 
6'4 
35 
14-1 
I2'3 
10-9 
70 
6*9 
6'5 
6-2 
36 
J 3'9 
12*1 
io-8 
7 1 
67 
6-3 
6*o 
37 
i 3'7 
ii-9 
10 6 
7 2 
6, 5 
6 -i 
5-8 
38 
J 3'5 
ii-8 
io-5 
73 
6-2 
5'9 
5-6 
39 
13‘3 
H-6 
10*4 
74 
5'9 
5 ' 6 
5-4 
40 
13-2 
U '5 
10-3 
75 
5-6 
5'4 
5'2 
The ufes of thefe Tables may be exemplified in the fol¬ 
lowing Problems. 
Prob. 1. To fnd the Probability, or Proportion of Chance, 
that a P erf on of a Given Age continues in being a propofed Num¬ 
ber of Years .—Suppofe the age be 40, and the number of 
years propofed 15 5 then, to calculate by the probabilities 
for London, in Tab. I. again!! 40 years (lands 214, and 
a train ft 55 years, the age to which the perfon mud arrive, 
lfands 120 "; which (hows that, of 214 perfons who attain 
to the age of 40, only 120 of them reach the age of 55, 
and consequently 94 die between the ages of 40 and 55. 
It is evident therefore that the odds for attaining the pro¬ 
pofed age of 55, are as 120 to 94, or as 9 to 7 nearly. 
Prob. 2. to fnd the Value of an Annuity for a propofed 
life. —This problem is refolved front Tab. II. by looking 
againlt the given age, and under the propofed rate of in¬ 
tereft j then the correfponding quantity (hows the number 
of years purchafe required. For example, If the given age 
be 36, the rate of intereft 4 per cent, and the propofed 
annuity 2501. Then in the Table it appears that the 
value is n'i years purchafe, or 12.1 times 250I. that is 
302 5I. ... 
After the fame manner the anfwer will be found in any 
other cafe falling within the limits of the Table. But, as 
there may fometimes be occafion to know the values of 
lives computed at higher rates of intereft than thqfe in 
the Table, the two following practical rules are lubjoined ; 
by which the problem is refolved independent of tables. 
"Rule i. When the given age is not lefs than 45 years, 
nor greater than 85, fubtraft it from 92 ; then multiply the 
remainder by the perpetuity, and divide the produft by 
the faid remainder added to 2A times the perpetuity ; fo 
{hall the quotient be the number of years purchafe required. 
Where note, that by the perpetuity is meant the number of 
3 
years purchafe of the fee-fimple; found by dividing 100 
by the rate per cent, at which intereft is reckoned. 
Ex. Let the given age be 50 years, and the rate of in- 
tereft 10 per cent. Then fubtracling 50 from 92, there 
remains 42 ; which multiplied by 10 the perpetuity, gives 
420; and this divided by 67, the remainder increafed by 
2-g times 10 the perpetuity, quotes 6-3 nearly, for the num¬ 
ber of years purchafe. Therefore, fuppofing the annuity 
to be iool. its value in prefent money will be 630I. 
Rule 2. When the age is between 10 and 45 years ; 
take 8-tenths of what it wants of 45, which divide by the 
rate per cent, increafed by 1*2; then, if the quotient be 
added to the value of a life of 45 years, found by the pre¬ 
ceding rule, there will be obtained the number of years 
purchafe in this cafe. For example, Let the propofed age 
be 20 years, and the rate of intereft 5 per cent. Here 
taking 20 from 45, there remains 25 ; fg of which is 20; 
which divided by 6-2, quotes 3-2; and this added to 9-8, 
the value of a life of 45, found by the former rule, gives 
i3forthe number of years purchafe that a life of 20 ought 
to be valued at. 
And the conclufions derived by thefe rules, Mr. Simp- 
fon adds, are (o near the true values, computed from real 
obfervations, as feldom to differ from them by more than 
•jAj or of one year’s purchafe. 
The obfervations here alluded to, are thofe which are 
founded on the London bills of mortality. And a fimilar 
method of folution, accommodated to the Bredau obfer¬ 
vations, will be as follows, viz. “Multiply the difference 
between the given age and 85 years by the perpetuity, 
and divide the product by 8-tenths of the faid difference 
increafed by double the perpetuity, for the anfwer.” 
Which, from 8 to 80 years of age, will commonly come 
within lefs than § of a year’s purchafe of the truth. 
Table 
