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 = Pert 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.