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To preface, I'm very, very new to Mathematica. I've written a few functions to calculate compound dividends from stocks.

compoundDivsInterest[shares_, divyield_, years_, compoundrate_] := 
   ((shares (1 + (divyield/compoundrate))^(compoundrate*years) - shares))

compoundDivsTotal[shares_, divyield_, years_,compoundrate_] := 
   ((shares (1 + (compoundrate))^(compoundrate*years)))

TL;DR: I can't seem to get these functions to graph their correct exponential form. I've tried using a sum, using Show[Table[Plot[..., For[...Plot[..., and a "recursive" function. None have worked so far. What should I do to get them to plot correctly?

As they are now, they will give the right value for a given x, but any other values are incorrect (as the function doesn't technically compound off the new principal). If I graph the functions, they are linear in nature.

A friend better versed in Mathematica than I suggested I use a sum to graph them. Plot[Sum[compoundDivsTotal[x, 0.0659, 1, 4], {x, 1, n, 1}],{n, 0,1000}]

This does yield an exponential curve as would be expected, but none of the values are correct.

In order to plot the correct, exponential graph of compounded interest, I figured it would probably have to be done recursively or iteratively. I've tried many different ways from google, such as Show[Table[Plot[..., and For[...Plot[.... Finally, I tried doing the closest thing I could find to recursion, which was to re-implement the function as:

recCompoundDivsTotal[shares_,divyield_,years_,compoundrate_] := 
 recCompoundDivsTotal[shares] = 
   ((shares (1 +(divyield/compoundrate))^(compoundrate * years)))

It gives the right value, but it's still linear in nature even though, from what I understand, it ought to recursively iterate using the previous value of shares

I'm at a loss for what to do. Any ideas?

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  • $\begingroup$ what is the parameters divyield? $\endgroup$ Jan 23, 2019 at 19:53
  • $\begingroup$ It's the dividend yield of the stock as a decimal percentage. In effect, the interest rate of the stock. $\endgroup$
    – vlca
    Jan 23, 2019 at 20:37
  • $\begingroup$ And divyield=? $\endgroup$ Jan 23, 2019 at 20:40
  • $\begingroup$ My bad. Use .0659. I've been calling the function using compoundDivsTotal[x, 0.0659, 1, 4] $\endgroup$
    – vlca
    Jan 23, 2019 at 20:45
  • $\begingroup$ So compoundrate = 4? It's a lot. $\endgroup$ Jan 23, 2019 at 21:20

1 Answer 1

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This is an option if the functions are defined correctly.

compoundDivsInterest[shares_, divyield_, years_, 
      compoundrate_] := ((shares (1 + (divyield/
              compoundrate))^(compoundrate*years) - shares))

compoundDivsTotal[shares_, divyield_, years_, 
  compoundrate_] := ((shares (1 + (compoundrate))^(compoundrate*
       years)))

{Plot[Evaluate[
   Table[compoundDivsTotal[10^n, 0.0659, t, .4], {n, 2, 3}]], {t, 0, 
   10}, AxesLabel -> {"t, years", ""}, 
  PlotLabel -> "Compound Dividends Total", PlotLegends -> Automatic], 
 Plot3D[Evaluate[
   Table[compoundDivsTotal[s, 0.0659, t, .4], {n, 2, 3}]], {t, 0, 
   10}, {s, 0, 1000}, AxesLabel -> {"t, years", "shares", ""}, 
  PlotLabel -> "Compound Dividends Total", Mesh -> None, 
  ColorFunction -> "Rainbow"]}

fig1

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