a) Justin won a contest at a local business that paid him a lump sum of $5,000. Justin, who just turned 22 years of age, has decided to invest his $5,000 for 45 years until he retires. During this time Justin believes that his account will earn 13% every year, compounded annually. As soon as he retires (exactly 45 years from today) Justin will start withdrawing retirement funds every year for an additional 33 years, but he plans to invest more conservatively at 8% compounded annually during retirement. How much can Justin withdraw each year in retirement?

b)Last week, Bayonetta opened a new wealth management account at the Capital Bank of Noatun to begin saving for retirement. Today, Bayonetta deposited $135,000 into her account. She then plans to make equal deposits into the account every month for the next 18 years (thus, Bayonetta will make a total of 216 equal deposits into her account with the first deposit to be made exactly one month from today). Exactly one month after her last deposit is made into the account, Bayonetta wants to withdraw $35,000 per month from the account for a total of 15 years (i.e., a total of 180 withdrawals). If Bayonetta believes she will earn 9.75% p.a. with monthly compounding on her account over the entire deposit and withdrawal period, what is the minimum amount that she must deposit every month during the deposit phase (i.e., for months 1 to 216) to achieve her withdrawal goal?