Review the Math Notes box in this lesson about continuously compounded interest.

1. Calculate the amount Tabitha had after investing her $$10,000$ for one year at $3\%$ annual interest, compounded continuously. How does this compare with her hourly compounding result of $$10,304.56$?

   Hint (a):

   Remember to simplify within the parentheses before solving the exponent.

2. Suppose a large investment group invested $10$ billion dollars at $8\%$ annual interest. Compare the amount they would have in one year if the interest were compounded continuously with the amount they would earn if the interest were compounded daily.

   Partial Answer (b):

   $$10,832,870, 680$ and $$10,832,775,720$
   Now find the difference.

3. Which investors might benefit from continuous compounding, rather than daily compounding?

   Hint: (c)

   Is it better to have a larger starting amount or a smaller amount?