An explicit model for predicting Dst based on solar wind data for the years 1995--1999 gives a good fit with a prediction efficiency of 88%, a linear correlation coefficient between the Dst index and the model of 0.94, and a RMS error of 6.4 nT. The same model applied to the first half of 2000 gave a prediction efficiency of 91%, a linear correlation coefficient of 0.95, and a RMS error of 7.9 nT. The modeled Dst is a sum of three terms that have growth and decay, a dynamic pressure term, an interplanetary magnetic field term, and some offset terms. The main innovations are that the decay terms have different time constants ranging from 5 days to 1 hour and that all the terms except the offsets depend on the angle of the Earth's dipole with respect to the solar wind velocity. This result shows that the magnetosphere is highly predictable and that chaotic behavior within the magnetosphere has little influence on the large-scale currents that determine Dst.