ES. 
and Babbage’s; the 
ct, as it contains the 
: COMPOUND INTEREST. 13 
As the excess of the amount at the end of the term above the original 
principal arises from the interest of money, we have this rule :—“ From 
the amount at the end of the term, subtract the original principal, and 
; to in 29 years at 
the difference is equal to the interest.” 
21. To find (p) the principal, the rest being given. 
£ £ £ 
31 __ 10 _ 1 
-100 " 300 30, 
By art. 19, s = p (1 + i) H 
dividing each side by (1 + i) n 
s 
p = (1 + *)“ = s (I + i)~ n 
Rule. Divide the given amount by the amount of ¿£l in the same 
term. 
Example. What principal will amount to £395,0394 in 4 years at 
5 per cent compound interest ? 
« — 395.0394, (1 + 0 = 1.05, n-4, by table 3, (1.05) 4 =1.215506 
1.215506)395.0394(325 
3646518 
904,200 = £904 4 0 
1 for any number of 
4. 4£. 5. 6. 7. 8. 9. 
des, published by him 
eater number of years 
be amount opposite to 
100; if the amount of 
1.03) 100 X (1.03) 30 = 
id 3 per cent we find 
n the same column 
1863198 X 2.42726247 
rs. As an example of 
303876 
243101 
60775 
60775 
This example is computed by contracted division, which cuts off one 
figure at each step from the divisor instead of annexing to the 
dividend. 
By logarithms. 
Art. 19, log s = p + n X log (1 + 0 
By transposition log p — log s — n x log (1 +0 
- log 1.05 = 1.9788107 
4 
5 per cent compound 
—7i log (1 + i) = 1.9152428 
log s = 2.5966406 
log j) = 2.5118834 ¿£325 
d 
22. To find (n) the number of years, the rest being given. 
To obtain this we must use the logarithmic formula 
rr; p inverted 
(Art. 19) log. s~ log^p + n log. (1 + i) 
By transposition n log (1 + i) = log s — log p 
dividing each side by log (1 -j- i) 
¿£395 0 93 
ual to the logarithm of that 
In the present instance the 
ve the decimal positive, we 
log s — log p 
n — — — 
log (1 + i) 
Rule. Find the difference between the logarithms of the. amount 
and of the principal, and divide by the logarithm of the amount of £ 1 
in one year. 
,52287875.