Math 108 Topics in Mathematics | James Baglama |
21.3 A Limit to Compounding - Video

21.3 A Limit to Compounding - Video

Key Ideas

Compounding interest more often results in a higher value in the account because interest is earned
earlier and is included with the principal in the next compounding period. However, the more often
interest is compounded, the less significant this increase becomes. The limit is reached when interest
is compounded continuously. The formula for finding the account balance when interest is
compounded continuously is A = Pe^{rt} where r is the nominal interest rate and t is the time in years.
e is a constant which is approximately equal to 2.718281828. The pattern of decimals does not repeat
and does not yield a rational number.

There is virtually no difference whether a bank treats a year as 365 days or 360 days. We will use
m = 365 if the money is to be compounded daily.