Consider a man who deposits his money in the amount of A0  $100 in a
savings account at an annual interest rate of 18 percent, and let us try to determine
the amount of money he will have after one year if interest is compounded
continuously (or instantaneously). In the case of simple interest, the
money will earn $18 interest, and the man will have 100  100  0.18 
$118.00 in his account after one year. But in the case of compounding, the
interest earned during a compounding period will also earn interest for the
remaining part of the year, and the year-end balance will be greater than $118.
For example, if the money is compounded twice a year, the balance will be
100  100  (0.18/2)  $109 after six months, and 109  109  (0.18/2) 
$118.81 at the end of the year. We could also determine the balance A directly
from