You wish to retire 30 years from today (in 2050). You will need $10,000 at the end of every month during your retirement to afford the lifestyle you desire, and you want to have enough money for 25 years in retirement. Your savings account will earn 1.5% annual percentage rate (APR) compounded monthly for the next 20 years due to the current environment of low interest rates. Starting in 2040, however, you believe interest rates will increase to 3% APR compounded monthly for the rest of your life.

a) How much do you need to deposit today in the account so that you have enough money to fund your retirement?

b) If you have no money now, how much money do you need to deposit at the end of each month for the next 20 years to completely fund your retirement at 2050?

Please solve and show work. Thanks!