is valued ; 
from unity, 
dished rates 
after having 
the annuity at 
656, the value 
Î12, and at age 
and 
, as before. 
ON THE 
VALUE OF ANNUITIES, 
8fc. 
SIMPLE INTEREST 
1. Is the sum paid for the use of the principal only, during the 
whole term of the loan, and varies (when the rate is the same) with the 
time, and the value of the loan; thus, the interest of £ 100 for one year, 
at 4 per cent per annum, is £4; the interest of the same sum for two 
years, is £8; the interest of twice the sum (¿£200) for one year is ¿£8, 
and for two years ¿£16. 
2. The sum of principal and interest in any given time is called the 
amount ; thus, in one year, the amount of ¿£100 at 4 per cent is ¿£100 
+ 4 = ¿£104. 
3. To obtain general rules for the solution of cases in Simple Interest, 
let us make 
s = the amount, 
p = the principal, 
n — the number of years, 
i = the interest of ¿£1 for one yeai expressed in decimal 
parts of a pound. 
4. To find (s) the amount. 
Multiplying i the interest of ¿£l for one year by p, we obtain ip the 
interest of £p for the same period; this multiplied again by n, gives 
inp, the interest of ¿£ p for n years. 
.*. s = p + inp r= p (1 + in) r= the amount. 
The following is the rule expressed in words : “ Multiply the interest 
of ¿£l for one year by the number of years, add one to the product, and 
multiply the sum by the principal.” 
5. Example. A agrees to lend B the sum of ¿£537 12 6 for 5 years, 
at an annual interest of 4 per cent; what sum must B pay at the expi 
ration of that period for principal and interest ?