In this work we extend the concept of uplink-downlink rate balancing to frequency division duplex (FDD) massive MIMO systems. We consider a base station with large number antennas serving many single antenna users. We first show that any unused capacity in the uplink can be traded off for higher throughput in the downlink in a system that uses either dirty paper (DP) coding or linear zero-forcing (ZF) precoding. We then also study the scaling of the system throughput with the number of antennas in cases of linear Beamforming (BF) Precoding, ZF Precoding, and DP coding. We show that the downlink throughput is proportional to the logarithm of the number of antennas. While, this logarithmic scaling is lower than the linear scaling of the rate in the uplink, it can still bring significant throughput gains. For example, we demonstrate through analysis and simulation that increasing the number of antennas from 4 to 128 will increase the throughput by more than a factor of 5. We also show that a logarithmic scaling of downlink throughput as a function of the number of receive antennas can be achieved even when the number of transmit antennas only increases logarithmically with the number of receive antennas.