$2.$ Luis has $$2$ million saved for retirement and wants to make sure he can spend $$100,000$ each year for the next $40$ years.

a$.$ He has no children, so he has no need to leave any savings when he expires. What interest rate must he get on his investment to be certain of this goal?

b$.$ He decides he wishes to leave $$200,000$ to charity when he dies. Now what interest rate must he achieve?