[list][br][*]Moveable point on vertical axis specifies Starting amount.[br][*]Nominal Annual Interest Rate is set with the top slider (between [math]-0.5[/math] and 0.5, in increments of 0.1).[br][*]Green diamonds show balances after 1,2,3, and 4 years of annually compounded interest.[br][*]Blue slider for M and checkbox enable a graph of account balance with compounding M times per year.[br][*]Red slider for N (increments of 4) and its checkbox does similar stuff.[br][*]The remaining checkbox will show a table with green, blue, red balances after 4 years.[br][/list]

[list][br][*]Use blue slider to choose M=1, then interpret the blue graph and the green diamonds.[br][*]Choose M=2, then interpret the new blue graph and the green diamonds (which did not move).[br][*]Choose M=3. Use blue graph to estimate balance at 2.5 years, then compute exact value.[br][*]Explore the effect of increasing the value of M.[br][*]Click on the red checkbox to display a red graph for compounding done N times per year.[br][list][br] [*]Choose M=2 (blue) and N=4 (red). Compare the blue and red graphs, interpret each and interpret the difference between them.[br] [*]Repeat previous comparisons but with M=4 and N=8.[br] [*]Choose M=4 and N=12. Display the table with balances at end of 4 years. Compute the balances at end of 4.5 years.[br][/list][br][*]Explore the effect of increasing the value of N.[br][*]Formulate a conjecture (informed guess) about the effect of increasing N beyond the max provided in this applet.[br][list][br] [*]If N is huge, why does the red graph resemble a continuous curve?[br] [*]What would be a good formula for such continuous curve? (Hint: try an exponential with a special base.)[br][/list][br][/list]