You are trying to decide how much to save for retirement. Assume you plan to save $$$$8$ comma $000$ per year with the first investment made one year from now. You think you can earn $5\%$ per year on your investments and you plan to retire in$33$years$,$ immediately after making your last $$$$8$ comma $000$ investment.

a$.$ How much will you have in your retirement account on the day you$$ retire?

b$.$ If$,$ instead of investing $$$$8$ comma $000$ per$$ year, you wanted to make one$$ lump$-$sum investment today for your retirement that will result in the same retirement$$ saving, how much would that lump sum need to$$ be$?$