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.)