$$ Assume you are now $21$ years old and will start working as soon as you graduate from college. You plan to start saving for your retirement on your $25$th birthday and retire on your $65$th birthday. After retirement, you expect to live at least until you are $85.$ You wish to be able to withdraw $$50,000($in today$$s dollars$)$ every year from the time of your retirement until you are $85$ years old $($i$.$e$.,$ for $20$ years$).$ The average inflation rate is likely to be $5$ percent. a$)$Calculate the lump sum you need to have accumulated at age $65$ to be able to draw the desired income. Assume that the annual return on your investments is likely to be $10$ percent. $($Round answer to $2$ decimal places, e$.$g$.15\mathrm{.}25.$ Do not round factor values.$)$ b$)$ What is the dollar amount you need to invest every year, starting at age $26$ and ending at age $65($i$.$e$.,$ for $40$ years$)$ to reach the target lump sum at age $65?($Round factor values to $4$ decimal places, e$.$g$.1\mathrm{.}5212$ and final answer to $0$ decimal places, e$.$g$.1,525.)$ ANSWER IS $5,441,358\mathrm{.}48$WHAT IS THE DOLLAR AMOUNT YOU NEED TO INVEST EVERY YEAR, STARTING AT THE AGE OF $26$ AND ENDING AT $65($ I.E$.$ FOR $40$ YEARS$),$ TO REACH TARGET LUMP SUM AT $65$ answer $$12,294\mathrm{.}28.$

Now answer parts a and b assuming the rate of return to be $8$ percent per year and $15$ percent per year $($ round to $0$ decimal places$)$