It depends on which Taekwondo association you train in, but it would usually take several decades to do it.
Firstly, the highest rank in Taekwondo is that of grandmaster, which corresponds to ninth degree black belt. It usually takes most of your life to reach the rank of grandmaster – see this question for more information on that.
The title of master is awarded at different levels of black belt in different organisations. Many organisations award the title of master at sixth or seventh degree black belt, but some award it at fifth degree black belt or even fourth. As such, how long it takes to reach the level of master in Taekwondo depends on the organisation.
Assuming that the title of master is awarded at sixth degree black belt, and assuming the same minimum progression times as in this question, it would take at least 17 years to become a master in Taekwondo. However, this assumes that you progress from one grade to the next in the shortest possible time, and that you pass every grading first time.