We present the exact and iterative solutions of the radial Schrodinger equation for a class of potentials, V (r) = A/r(2) - B/r+Cr-k, for various values of k from - =2 to 2, for any n and l quantum states by applying the asymptotic iteration method. The global analysis of this potential family by using the asymptotic iterationmethod results in exact analytical solutions for the values of k = 0,- 1 and -2. Nevertheless, there are no analytical solutions for the cases k = 1 and 2. Therefore, the energy eigenvalues are obtained numerically. Our results are in excellent agreement with previous work.