Suppose that you are $22$ years old, and have just accepted a job as an investment banking analyst in New York, at a starting salary of $$125,000$ per year. You intend to work for $30$ years and to retire at $52.$ During retirement, you intend to withdraw monthly from your retirement savings for $35$ years. You expect that during retirement, you will need $$10,000$ at the start of every month, after tax $($assume you will pay tax at a rate of $20\%$ on all the monthly withdrawals$).$ Assume that you can earn $8\%$ per year APR on your investments.

a$)$ How much money would you need to have in your retirement accounts, when you retire?

b$)$ How much would you have to save at the end of every month during your working life, if you intend to save the same monthly amount?