our grandparents just gave you $$40,000$ for your $21$st birthday. You want to set aside some

of that money so you can withdraw $$1,500$ per month for living expenses for the $20$ months

you attend BCIT and still have $$7,000$ left at the end of the $20$ months to pay for a trip after

graduation. Your first withdrawal will be $1(1)/(2)$ years from now when you start BCIT. Assume

both the money set aside and the annuity earns $6\%$ compounded quarterly.

$($a$)$ How much of the $$40,000$ must you set aside? $($b$)$ How much interest will you earn