ig. 2*75.) 
z 2 — &c. 
rery little 
er powers 
1 - 19 X .0324828- 1.0324828 
of i; and 
re may be 
ating the 
sold at 19 
rin for his 
t. 
- .0000513 
19 - 30 (1.0324828)- 31 
i .0324828 - .0000513 = .0324315 = interest of £l 
.0324315 X 100 = 3.24315 = £3 4 10| per cent. 
55. When interest is convertible m times a year, and the annuity 
payable m' times, each payment being the present value of the first 
payment is 
m'n, and the present value of the annuity is the sum of the series 
where the first term is ( 1 4 ) m ', the common ratio (1+ 2 
\ m J \ m y 
and the number of terms m'n, which being substituted in the formula 
a -, as in Art. 49., the present value of the annuity becomes 
multiplying numerator and denominator by ( 1 +