18 
ON THE VALUE OF ANNUITIES. 
and the amount of ¿£l in the example, is only .00081, or .243 for ¿£300, 
which is very inconsiderable; but in the latter example, the amount of 
¿£l in 40 years, interest payable yearly, is 4.80102, shewing a dif 
ference of .15201 in the amount of ¿£l for that time, or for the sum of 
¿£300 a difference equal to ¿£45,603. 
29. To find (p) the principal. 
f i\ mn 
Art. 24, < = p(l+-) 
by logarithms, log p = log s - mn x log (b + ^ J 
Rule. Divide the given amount by the amount of ¿£l in the time. 
Example. What sum will amount to ¿£690 in 15 years at 8 per 
cent compound interest payable quarterly ? 
s = 690, n — 15, m = 4, i 
1 + — ) = (1.02) 60 r= 3.281031 by Table 3, under 2 per cent 
m. 
3.281031)690 (210.299 = ¿£210 6 0 
.... 6562062 
331938 
9835 
'6562 
3213 
2953 
320 
295