4. a. You plan to retire in 20 years. At that point, you want to have $100,000 saved up. Interest rates in your savings account will remain constant at 6% p.a., compounded semi-annually. If you put $32,000 into this account now, will you reach your goal of $100,000? Prove your answer with the figures.

b. If your answer to a is "no", please find out how much would have to be put into the account now, to meet the $100,000 goal. If your answer to a is "yes", then do not answer b.