This paper studies the optimal investment strategies of maximizing expected utility from terminal wealth.According to the fact that the borrowing rate is higher than the saving rate,and by adoption of the utility function of U(x)=x~ρ/ρ,0<ρ<1 for the investor,we develop a new method of Guess-Verify instead of stochastic dynamic programming with It formula and nonlinear programming technique to solve the optimal investment strategies,which is easy to handle.