Topic Two: Comprehensive Examples

Q$3$ Retirement planning

You want to start funding your retirement. You plan to do this by making $40$ semi$-$annual deposits of $$3,000$ beginning today, your ${30}^{th}$ birthday. After that you do not plan to save any more. You expect to earn an APR of $12\%$ compounded monthly from now until you retire.

You plan to retire on your ${65}^{th}$ birthday, and live until you are almost $85($dying the day before your ${85}^{th}$ birthday$).$ Your first monthly withdrawal is on your ${65}^{th}$ birthday $($and the last withdrawal is the month before you are $85).$ After retirement you expect to earn an effective annual rate $($EAR$)$ of $9\%.$ How much can you with draw each month?