The uplink of a pilot-assisted code-division multiple access system is considered where the pilot symbols are time-multiplexed with the data symbols. The channel is modeled to be varying with each chip. Lower and upper bounds on the sum-capacity are obtained. Optimal pilot-to-data symbol rates are observed numerically. It is observed that with fixed spreading gain and increasing traffic load, channel estimation deteriorates, but the capacity increases for small traffic loads and decreases for large traffic load. The optimal value of traffic load is observed to be around unity, in agreement with previous work. It is also observed that with increasing spreading gain and fixed traffic load, the capacity converges to a value.