# compound interest

Author:
Dick Lane
• Moveable point on vertical axis specifies Starting amount.
• Nominal Annual Interest Rate is set with the top slider (between and 0.5, in increments of 0.1).
• Green diamonds show balances after 1,2,3, and 4 years of annually compounded interest.
• Blue slider for M and checkbox enable a graph of account balance with compounding M times per year.
• Red slider for N (increments of 4) and its checkbox does similar stuff.
• The remaining checkbox will show a table with green, blue, red balances after 4 years.
• Use blue slider to choose M=1, then interpret the blue graph and the green diamonds.
• Choose M=2, then interpret the new blue graph and the green diamonds (which did not move).
• Choose M=3. Use blue graph to estimate balance at 2.5 years, then compute exact value.
• Explore the effect of increasing the value of M.
• Click on the red checkbox to display a red graph for compounding done N times per year.
• Choose M=2 (blue) and N=4 (red). Compare the blue and red graphs, interpret each and interpret the difference between them.
• Repeat previous comparisons but with M=4 and N=8.
• 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.
• Explore the effect of increasing the value of N.
• Formulate a conjecture (informed guess) about the effect of increasing N beyond the max provided in this applet.
• If N is huge, why does the red graph resemble a continuous curve?
• What would be a good formula for such continuous curve? (Hint: try an exponential with a special base.)