1. The Powerball today, August 24, 2020, is $37 million with a lump sum payout of $29.6 million. Calculate the after-tax return on a $2 ticket for the lump sum payout using the probability of winning and tax rates given in the text.

2. Assume you get a job paying $55,000 per year after graduation; calculate your disposable income, average tax rate, and marginal tax rate.

3. Assume you expect to live 20 additional years after you retire as college educated people tend to live longer than the average person and believe you will need $182,839 per year to live comfortably (equal to $75,000 today) or $3,716,780 total. How much will you need to save per month over your 46 working years if you invest in investments that yield 5% and 9%?