Embarrassing but true: basic algebra eludes me, how do I solve this equation?
There is (probably) no formula for the problem you are trying to solve. The equation you have to start with is a polynomial equation of degree n in q, which, in general has no algebraic solution for n larger than 4. What you need to do here is use an iterative solution technique, where you guess the answer, see how close it is, and modify your guess to make it closer. The easiest way of doing this is to use Newton’s Method. In Excel, it goes something like this: • Rearrange your formula so that one side is only zero, and call this function f(q)=pv*(1+r)n+pmt*((1+r)n-(1+q)n)/(r-q) – fv so that f(q) is zero when you put in the right q. • Make an initial guess q0 (It doesn’t actually have to be a good guess) • Evaluate f(q0) using the formula. • Evaluate f(q0+dq) where dq is some small number, say 10-6. • Evaluate the derivative, f'(q0)=[f(q0+dq)-f(q)]/dq • Make a new guess, q1=q0 – f(q0)/f'(q0) • Repeat this procedure using th
