Complete these problems with steps:

1. Your mother just won $250,000 for splitting a Nobel Prize equally with three other co-workers. If she invests her prize money in a diversified equity portfolio returning 8 percent per year, approximately how long will it take her to become a millionaire, before accounting for taxes?

2. Jill received a 30,000 inheritance. She wants to save up for a down payment for her first home to be purchased 8 years from now. If she can earn 5% on her savings per year how much of the inheritance does she need to save now to make a $20,000 down payment 8 years from now?

3. Richard is 65 years old and about to retire. He has $500,000 saved to supplement his pension and social security and would like to withdraw his savings in equal dollar amounts so that nothing is left after 15 years. How much does he have to withdraw each year if he earns 7 percent on his money?

4. Monica, 22 just started working full time and plans to deposit $3,000 annually into a Roth IRA earning 12 percent interest compounded annually. How much would she have after 20 years, 30 years, and 40 years? If she decided to make monthly payments of $250 per month instead of the $3,000 each year would she end up with more or less money at the end of 40 years (assuming interest was compounded monthly)? If she had a 30% tax rate when she took the money out 40 years from now how much in taxes would she have to pay?