Reverberation time, T60, directly influences the amount of reverberation in a signal, and its direct estimation may help with dereverberation. Traditionally, T60 estimation has been done using signal processing or probabilistic approaches, until recently where deep-learning approaches have been developed. Unfortunately, the appropriate loss function for training the network has not been adequately determined. In this paper, we propose a composite classification- and regression-based cost function for training a deep neural network that predicts T60 for a variety of reverberant signals. We investigate pure-classification, pure-regression, and combined classification-regression based loss functions, where we additionally incorporate computational measures of success. Our results reveal that our composite loss function leads to the best performance as compared to other loss functions and comparison approaches. We also show that this combined loss function helps with generalization.