Assume you are now $21$ years old and will start working as soon as you graduate from college. You plan to start saving for your retirement on your $25$th birthday and retire on your $65$th birthday. After retirement, you expect to live at least until you are $85.$ You wish to be able to withdraw $$37,000($in today's dollars$)$ every year from the time of your retirement until you are $85$ years old $($i$.$e$.,$ for $20$ years$).$ The average inflation rate is likely to be $5$ percent. Problem $6\mathrm{.}42($a$)$ Calculate the lump sum you need to have accumulated at age $65$ to be able to draw the desired income. Assume that the annual return on your investments is $\_\_\_\_\_\_$