An Individual Retirement Account $($IRA$)$ is an account in which the saver does not pay income tax on the amount deposited but is not allowed to withdraw the money until retirement. $($The saver pays income tax at that point, but his or her tax bracket is much lower then.$)$

Marlene Silva wishes to have an IRA that will be worth $$100,000$ when she retires at age $65.($Round your answers to the nearest cent.$)$

$($a$)$ How much must she deposit at age $37$ at $8\frac{3}{8}\%$ compounded daily?

$($b$)$ If$,$ at age $65,$ she arranges for the monthly interest to be sent to her, how much will she receive each thirty$-$day month?