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 $$48,000($in today's dollars$)$ 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$)$

Your answer is incorrect.

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 likely to be $10$ percent. $($Round answer to $2$ decimal places, eg$.15\mathrm{.}25.$ Round intermediate value to $3$ decimal places, e$.$g$.359400\mathrm{.}312.$ Do not round factor values.$)$

Lump sum amount accumulated at age $65$$