22 
ON THE VALUE OF ANNUITIES. 
for different rates of interest, by multiplying this by the number of years, 
we find the logarithm of £l in that term. 
The following table gives the amounts and their logarithms of £l in 
one year, payable yearly, half-yearly, quarterly, and momently, for dif 
ferent rates of interest, and is thus formed: 
When interest is 3^ per cent, the amount payable yearly is 1.035, 
the logarithm of which is .0149403497, (Hutton’s Logs., Table 3); 
when interest is payable half-yearly we have 
. . 31 Y / 7 V f407 N 
1 + 
= 1 + 
100 X 2, 
= 1.035306 
= 1 + 
400 
400 
log 
'407 N 
.400, 
= 2{log 407 - log 400} 
= 2(2.6095944092 — 2.6020599913} *0150688358; 
when interest is payable quarterly 
1 + ~ 1 = ( i + -^7T ) = fh+ 1 
807 n 
100 X 4 ) 
= 1.035462; 
800 
807 
800 
log (§55 I = 4 i lo s 80,7 " log 800 ^ 
= 4(2.9068735347 - 2.9030899870} = .0151341908. 
When interest is payable momently, we have *035 X *4342944819 
“ *01520030687 for the logarithm, the number corresponding to 
which is 1.035620 
Nominal 
rate of 
Interest. 
Payable. 
Amount 
of ¿£1 in 
one year. 
Logarithms of 
such amount. 
Nominal 
rate of 
Interest. 
L 1 
Amount 
Of it'1 in 
one year. 
Logarithms of 
such amount. 
y 
1.020000 
.0086001718 
y 
1.050000 
.0211892991 
2 
h 
1.020100 
,0086427476 
5 
h 
1.050625 
.0214477308 
per cent. 
q 
1.020150 
.0086642470 
per cent. 
q 
1.050946 
.0215801275 
m 
1.020201 
.0086858896 
m m 
1.051271 
.0217147241 
y 
1.025000 
.0107238654 
y 
1.060000 
.0253058653 
n 
h 
1.025156 
.0107900638 
6 
h 
1.060900 
.0256744494 
per cent. 
q 
1.025235 
.0108235735 
per cent. 
q 
1.061364 
.0258641690 
m 
1.025315 
,0108573620 
m 
1.061837 
.0260576689 
y 
1.030000 
.0128372247 
y 
1.070000 
.0293837777 
3 
h 
1.030225 
.0129320845 
7 
h 
1.071225 
.0298806996 
per cent. 
q 
1.030339 
.0129802193 
per cent. 
9 
1.071859 
.0301376716 
m 
1.030454 
.0130288345 
m 
1.072508 
.0304006137 
y 
1.035000 
.0149403498 
y 
1.080000 
.0334237555 
3* 
k 
1.035306 
.0150688358 
8 
à 
1.081600 
,0340666786 
per cent. 
q 
1.035462 
.0151341909 
per cent. 
q 
1.082432 
.0344006870 
m 
1.035620 
.0152003069 
m 
1.083287 
.0347435586 
y 
1.040000 
.0170333393 
y 
1.090000 
.0374264979 
4 
h 
1.040400 
.0172003435 
9 
y 
1.092025 
.0382325809 
per cent. 
q 
1.040604 
.0172854951 
per cent. 
q 
1.093083 
.0386532667 
m 
1.040811 
.0173717793 
m 
1.094175 
.0390865034 
y 
1.045000 
.0191162904 
y 
1.100000 
.0413926852 
4* 
h 
1.045506 
.0193266334 
10 
h 
1.102500 
.0423785981 
per cent. 
q 
1.045765 
.0194341385 
per cent. 
q 
1.103813 
.0428954616 
in 
1.046028 
.0195432517 
m 
1.105171 
.0434294482 
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