We analyze the yearly mean sunspot-number data covering the period 1700 to 2012. We show that the yearly sunspot number is a low-dimensional deterministic chaotic system. We perform future predictions trying to forecast the solar activity during the next five years (2013 -aEuro parts per thousand 2017). We provide evidence that the yearly sunspot-number data can be used for long-term predictions. To test and prove that our model is able to predict the Maunder Minimum period (1645 -aEuro parts per thousand 1715), we perform long-term post-facto predictions comparing them with the observed sunspot-number values. We also perform long-term future predictions trying to forecast the solar activity up to 2102. Our predictions indicate that the present Cycle 24 is expected to be a low-peak cycle. We conclude that the level of solar activity is likely to be reduced significantly during the next 90 years, somewhat resembling the Maunder Minimum period