A proof of convergence is presented for a simplified numerical integration method for solving systems of correlated stochastic differential equations describing mean reverting geometric Brownian motion. Such systems arise in modelling the time evolution of interest rate term structures. For time discretization of size Delta t , the method leads to global error in time of O (Delta t2) and no error accumulation. The result is shown to extend to the case when principal components analysis is used to reduce the number of underlying stochastic factors.