Jerome's financial advisor is setting up a retirement income fund for him. When he turns $71,$ Jerome will use his investments to draw a monthly income. He wants to be able to withdraw $$3000$ at the end of each month from this fund. His investments currently earn $7\%$ per year, compounded monthly. $($PV Annuity$)$

a$)$ If he wants his savings to last for $24$ years $($until he turns $95),$ determine the amount he will need to have in the fund by the time he reaches age $71.($PV Annuity$)$

b$)$ Calculate the total income his fund will generate over the $24$ years.