A few points:-
(1) You should be using the Bisection Method for simple annuity problems. It is has no convergence problems if set up properly. (if this is a class project tell your instructor that)
http://en.wikipedia.org/wiki/Bisection_method(2) I am assume the interest is being payed every 3 months and is compounded. You need the equivalent annual rate?
(3) Is the $9874.60 at 24 months, ie at the time of the last payment or at 27 months?
