COMPOUND INTEREST. 
11 
3. 
3^ per cent simple 
of an annuity of £l 
irs 
£50 
,vill be found of great 
, square roots, cube 
D00, with other tables, 
to mathematics and 
being received as it 
the sum each year on 
be put out at Com- 
l of being taken up at 
added to the principal, 
ts interest amounts at 
jain forms a new prin- 
t the end of the third 
one year; 
the first year, and the 
i the same proportion, 
i. e. as 1 is to 1 + i, so is any sum, to its amount, in one year; and 
since 1 -+ i forms a new principal, its amount in one year gives the 
amount of £l, the original principal at the end of the 2nd year. 
1 : l + i :: l + i 
i : (1 + o : : (1 + *) 
1 : l+i :: (1 + if : (1 + if ditto 4th year, 
and proceeding in the same manner the amount of £l at the end of the 
ri h year is (1 + i) ”; this multiplied by p gives 
s “ yj (1 -f- i) n “ the amount of £p in n years, 
log s = logy> + n log (1 + i). 
Ride. Raise the amount of £l at the end of the first year, to the 
same power as the number of years, and multiply the result by the 
principal. 
Example. What is the amount of £325 in 4 years at 5 per cent 
compound interest ? 
p - 325 n = 4 1 + i = 1.05. 
1.05 
1.05 
5 25 
105 
1. 1025 = (1.05) 2 
1. 1025 
55125 
22050 
11025 
11025 
1. 21550625 = (.105) 4 
523 
3646518 
243101 
60775 
395.0394 = £395 0 9J 
In this example the amount of £l in 4 years is multiplied by what is 
termed contracted multiplication, the rule for which may be found in 
(Arithmetic and Algebra, Art. 167). 
Calculation by logarithms. 
Log s ns log p + n log (1 + i). 
Log (1 + i) == log 1.05 = 0.0211893 
n ~ 4 
n log (1 + i) = 0.0847572 
log 325 = 2.5118834 
log p + n log (1 + i) = 2.5966406 395,0394 = £395 0 9J 
Rules for logarithmic calculations may be found prefixed to nearly all 
the different collections of tables of logarithms, among the best and most 
g j amount of £l at the 
| end of the 2nd year. 
(1 -p j) 3 ditto 3rd year.