Many pension plans and private retirement products contain annuity factors, converting the funds at some future time into lifelong income. In general model settings like, for example, the Li-Lee mortality model, analytical values for the annuity factors are not available and one has to rely on numerical techniques. Their computation typically requires nested simulations as they depend on the interest rate level and the mortality tables at the time of retirement. We exploit the flexibility and efficiency of feed-forward neural networks (NNs) to value the annuity factors at the time of retirement. In a numerical study, we compare our deep learning approach to (least-squares) Monte-Carlo, which can be represented as a special case of the NN.