The article extends a model for interest rates by adding a flexible component to match different term structures. It uses random factors to capture variability and has nonnegative interest rates. The model provides fast solutions for forward rates, futures rates, and interest rate options. It is easy to implement and allows for pricing of complex derivatives. The model is Markovian, meaning interest rate distribution each period depends on current state variables. Nodes in a lattice model recombine, making it efficient. The model is calibrated to initial term structures in Treasury and Eurodollar markets.