1. Choose a value for k from the table based on the first letter of your last name for the investment
that you want to simulate, and set up your equation for T(r). Choose a value of k that is different
from your classmates values of k.
First letter of your last name Values for k Interpretation
AF 1.101.90 Investment will grow 1.10 to 1.90 times
GL 2.102.90 Investment will grow 2.10 to 2.90 times
MR 3.103.90 Investment will grow 3.10 to 3.90 times
SZ 4.104.90 Investment will grow 4.10 to 4.90 times
2. Find the derivative of T(r) with respect to r, the rate of change in time with respect to the interest
rate using the quotient rule. (Note that ln(k) is a constant.)
3. Choose 5 interest rates between 2% and 20%. Complete the following table by calculating the
values of T(r) and T(r), correctly rounded to two decimal places. (Note that the rates do not
necessarily have to be whole numbers. Examples such as 5.5% or 9.85% are acceptable.)
Interest Rates, r T(r) T(r)Page 2 of 3
4. What can you say about the values that you calculated with the interest rates that you have
chosen?
5. Show that your interpretation is correct by sketching the graph of T(r) and T(r) using Excel or
another graphing utility. (If necessary, the graphs may be pasted into a Word document and
attached to the DB thread.)
6. Compare your calculations to any of your classmates. Explain how different values for k and r
affect your calculations.
7. Which intellipath Learning Nodes helped you with this assignment?
The following are the steps to derive the formula in this assignment from the formula for compounding
interest at discrete periods of time, ???? = ????(1 + ????
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