Imagine you just earned your MBA degree. According to The Economist MBA Finder the average starting salary for Goodman MBA graduate is about $$120,000$ per year. Suppose you just got hired at this salary and decide to start planning for your retirement. You plan to work $30$ years before retirement and to live $20$ years after retirement. Prior to retirement, you will earn $10\%$ with monthly compounding by investing in stock index funds. During retirement, you plan to invest mostly in dividend paying stocks earning $5\%$ return with quarterly compounding. a$)$ If you invest $10\%$ of your monthluy salary at the end of each month, how much money will you accumulate by the retirement date? Assume that your annual salary of $$120,000$ is paid in equal monthly payments and, for simplicity assume no growth in salary over the next $30$ years.

After retirement, you will make equal annual withdrawals from your investment fund at the beginning of each year. In addition, you would like to have $$200,000$ at the end of your life $(20$ years after retirement$)$ just in case if you happen to live longer or decide to leave some inheritance for your grandchildren. Given this scenario, how much will you be able to withdraw at the beginning of each year during your retirement?