Fundingaretirementgoal.ChrisJoneswishestohave$$800,000$inaretirementfund$20$years from now. He can create the retirement fund by making a single lump$-$sum deposit today.a$.$ If he can earn $6$ percent on his investments, how much must Chris deposit today to createthe retirement fund? If he can earn only $4$ percent on his investments? Compare and discussthe results of your calculations.b$.$ If$,$ upon retirement in $20$ years, Chris plans to invest the $$800,000$ in a fund that earns$4$ percent, what is the maximum annual withdrawal he can make over the following $15$years?c$.$ How much would Chris need to have on deposit at retirement to annually withdraw $$35,000$over the $15$ years if the retirement fund earns $4$ percent?d$.$ To achieve his annual withdrawal goal of $$35,000$ calculated in part c$,$ how much more thanthe amount calculated in part a must Chris deposit today in an investment earning $4$ percent annual interest?

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