::
OK. I figured it out. I was right it was silly and easy. Use the distributive property. All the PMT/(1+Z) terms can be rewritten as PMT x (1/1+Z1) + PMT x (1/(1+Z2)^2) + … PMT x (1/(1+ZN)^N + 100 x (1/(1+ZN)^N. All the 1/1+Z terms can be grouped so you get PMT ((1/1+Z1) + (1/(1+Z2)^2 + etc.) + 100 x (1/(1+ZN)^N = 100. The last term is the face value discounted for N periods. Solve all the 1/Z terms and the 100/(1+ZN)^N. So you get PMT = (100 – (100/(1+ZN)^N))/(the sum of all the 1/1+Z terms)
Sorry if I wasted anyone’s time.