Let A=(17663.7-25000)/15247=-0.4812 approx, and x=1/(1+r), this equation can be written:
A=x+x^2+x^3+x^4=x(1-x^4)/(1-x) using the formula for the sum of terms for a geometric progression. Clearly x≠1 because that would make A=4.
Since A is a negative value, the expression in x must also be negative. When x<-1 or x>0 the expression is positive. Therefore, if there is a solution, it must be when -1<x<0. When x=-0.6058 approx the expression is -0.3264 which is 0.8076 short of A. Since r=1/x-1, r=2.6506 when x=-0.6058. This value of r is the closest to solving the equation, but it does not fulfil the equation because the right-hand side of the original equation is bigger than 25000. The equation has no solution for r.