14 ON THE VALUE OF ANNUITIES. 
Example. In how many years will ¿£325 amount to £395.0394 at 
5 per cent compound interest ? 
s = 395.0394 p = 325 1 + * = 1.05 
log 395.0394 = 2.5966406 
log 325. = 2.5118834 
log 1.05 = .0211893)0.0841572(4 years 
0847572 
23. To find (i) the rate of interest. 
Art. 19. s = p(l + 0" 
(1 + iY = 
P 
dividing each side hyp 
Extracting the n th root of each side, 1 -f i = ( — 
V 
By transposition i = ^ 71 — 1 
The readiest way of finding ^—j n is by logarithms, 
loo- (_f_Y ~ lo S * ~ lo SP 
a \pJ n 
Rule. Divide the difference between the logarithms of the principal 
and of the amount, by the number of years, and from the number cor 
responding to the quotient subtract one, the result is the interest of ¿£l; 
this multiplied by 100 gives the rate per cent. 
Example. At what rate per cent will £325 amount at compound 
interest to £395.0394 in 4 years ? 
w = 4 s = 395.0394 
log s = 2.5966406 
logp = 2.5118834 
4)0.0847572 
log .s — log p _ 0.0211893 
p = 325 
1.05 
1 
.05 = * 
100 
5 per cent. 
24. When interest is payable half-yearly, quarterly, &c. 
If the intervals at which interest is receivable be shorter than a 
year, and at each interval the interest be added to the principal as it 
becomes due, the amount at compound interest will evidently be greater