30 ON THE VALUE OF ANNUITIES. 
Nominal 
rate of 
Interest. 
Payable. 
Present 
value 
of ¿£1 in 
one year. 
Logarithm of 
such present 
value. 
Nominal 
rate of 
Interest. 
Payable. 
Present 
value 
of £\ in 
one year. 
Logarithm of 
such present 
value. 
y 
.980392 
T. 9913998282 
y 
.952381 
T.9788107009 
2 
h 
.980296 
T. 9913572524 
5 
h 
.951814 
1.9785522692 
per cent 
? 
.980247 
1.9913357530 
per cent 
y 
.951524 
T.9784198725 
m 
.980199 
T.9913141104 
m 
.951230 
T.9782852759 
y 
.975610 
Î. 9892761346 
y 
.943396 
T. 9746941347 
â| 
h 
.975461 
f. 9892099362 
6 
h 
.942596 
T. 9743255506 
per cent 
y 
.975386 
1.9891764265 
per cent 
y 
.942184 
T.9741358310 
m 
.975310 
r.9891426380 
m 
.941764 
T. 9739423311 
y 
.970874 
1~. 9871627753 
y 
.934579 
T.9706162223 
3 
h 
.970662 
T.9870679155 
7 
h 
.933511 
T. 9701193004 
per cent 
y 
.970554 
l". 9870197807 
per cent 
y 
.932958 
F. 9698623284 
m 
.970445 
IT. 9869711655 
m 
.932394 
T.9695993863 
y 
.966184 
r. 9850596502 
y 
.925926 
1.9665762445 
QJL 
0t 2 
k 
.965898 
T. 9849311642 
8 
h 
.924556 
T.9659333214 
per cent 
y 
.965752 
T. 9848658091 
per cent 
y 
.923845 
T.9655993130 
m 
.965605 
T. 9847996931 
m 
.923116 
T.9652564414 
y 
.961538 
T.9829666607 
y 
.917431 
T. 9625735021 
4 
h 
.961169 
1.9827996565 
9 
h 
.915730 
T.9617674191 
percent 
y 
.960980 
1.9827145049 
per cent 
y 
.914843 
1.9613467333 
m 
.960789 
1.9826282207 
m 
.913931 
T. 9609134966 
y 
.956938 
1.9808837096 
y 
.909091 
1.9586073148 
h 
.956474 
n9806733666 
10 
h 
.907029 
1.9576214019 
per cent 
y 
.956238 
1.9805658615 
per cent 
y 
.905950 
1.9571045384 
m 
.955997 
1.9804567483 
m 
.904837 
T.9565705518 
AMOUNT OF ANNUITIES AT COMPOUND INTEREST. 
45. We now proceed to consider cases in Annuities where compound 
interest is allowed. 
Let s = the amount of the annuity, 
a = the annuity, 
n — the number of years, 
i = interest of £l per annum. 
From what has been shewn in treating of the amount of Annuities at 
simple interest, in Art. 14, it appears that the amount of an annuity 
of £l in n years is found by summing the respective amounts of £l at 
the end of 0,1,2, 3,4,5, &c. to (n — 1) years. The amount of £l 
received at the end of 0 years after due, i. e. received immediately when