How can I solve this complicated custom function numerically?

Question

I have a complicated function that calculates the total value of payments from an account into which deposits are made annually. I'd like to solve the function for a growth rate numerically, but NSolve and FindRoot run for hours without returning a solution. This is the function:

    CalcDonation[seed_, growthrate_, reinvestrate_, annualcontrib_, horizon_] :=
     Module[{balance = 0, earnings, reinvestamount = 0, donation = 0},
      For[year = 1, year <= horizon , year++,
       (* No annual contribution in first year *)
       balance += If[year == 1, seed, annualcontrib + reinvestamount];
       earnings = balance * growthrate;
       reinvestamount = earnings * reinvestrate;
       donation += earnings *(1 - reinvestrate);
     ];
    donation
   ];

These are the attempts I have made so far:

FindRoot[CalcDonation[5000, g, 0.50, 1200, 36] == 5000 + 36*1200, {g, 0.05}]
NSolve[CalcDonation[5000, g, 0.50, 1200, 36] == 5000 + 36*1200, g, Reals]

Using Manipulate, I can approximate the answer as 0.0656782 (which is how I decided to use 0.05 as the starting point for FindRoot), but is there a way to solve this equation to a certain precision, besides FindRoot and NSolve? If not, how can I use these functions more effectively?

I'm not sure if this question has an answer that I can apply, since the question applies few details about the asker's situation.