



 
Darrin, A lot of the complications here are in blocks that you can keep together. Thus we can think instead about 1 / [1  (1 + D/12)^T] = (1 / D) * Q  R Q depends on B,P,T,Y,N,Z; R on Z,T,F. It's not too hard to see that by selecting appropriate Y and F (say) we can get any value for Q,R. So this really is generic. Now isolate the exponential term (1+D/12)^{T} on one side. You will probably spot one rather simple solution easily. If you plot both sides as functions of D, you should be able to show (if all constants in the original are positive) that one side goes to infinity for D=Q/R; that there is no other solution with 0<D<Q/R ; and that there is always a second solution with D > Q/R , and no other. Details are left to you. It seems to me almost certain that the second solution will not be expressible in closed form. Is it possible that a numerical solution is expected? Good hunting!
 


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 