You have finished your time at Kelley and need to start thinking about retirement. You plan on working for 30 more years and then retire. Upon your retirement 30 years from today, you plan to have enough money to withdraw $75,000 every 6 months, with the first payment coming exactly six months after your retirement day. You expect your retirement account to earn a return of 8% APR (stated rate), compounded quarterly, on all funds in the retirement account. Assume you want to draw on the retirement fund for 20 years after your retirement (40 semiannual withdrawals), and you want to fund the account with annual level payments, with the first payment being made one year from today and the last payment occurring the day of your retirement (30 total payments into the retirement account).

a) How much do you need in the account on your retirement day to fund the expected semiannual withdrawals?

b) How much does each annual payment need to be for the next 30 years to fund the retirement account?