We use a model for sunspot number using low-frequency solar oscillations, with periods 22, 53, 88, 106, 213, and 420 years modulating the 11-year Schwabe cycle, to predict the peak sunspot number of cycle 24 and for future cycles, including the period around 2100 A.D. We extend the earlier work of Damon and Jirikowic (1992) by adding a further long-period component of 420 years. Typically, the standard deviation between the model and the peak sunspot number in each solar cycle from 1750 to 1970 is ±34. The peak sunspot prediction for cycles 21, 22, and 23 agree with the observed sunspot activity levels within the error estimate. Our peak sunspot prediction for cycle 24 is significantly smaller than cycle 23, with peak sunspot numbers predicted to be 42 ± 34. These predictions suggest that a period of quiet solar activity is expected, lasting until ∼2030, with less disruption to satellite orbits, satellite lifetimes, and power distribution grids and lower risk of spacecraft failures and radiation dose to astronauts. Our model also predicts a recovery during the middle of the century to more typical solar activity cycles with peak sunspot numbers around 120. Eventually, the superposition of the minimum phase of the 105- and 420-year cycles just after 2100 leads to another period of significantly quieter solar conditions. This lends some support to the prediction of low solar activity in 2100 made by Clilverd et al. (2003).