Bill makes annual deposits of $$1600$ to an IRA earning $15\%$ compounded annually for $20$ years. At the end of the $20$ years Bill retires.

a$)$ What was the value of Bill's IRA at the end of $20$ years?

Value of IRA $=$ $

b$)$ What is the largest amount Bill may withdraw annually for the next $21$ years at $15\%$ compounded annually?

Payment $=$ $