You have decided to start saving for retirement. Your bank is willing to set you up with an IRA with a

$9\mathrm{.}2\%$ APR. You need to have $$925,000$ in the account in $45$ years to be able to retire.

$2$a$.$ How much of your remaining monthly budget do you want to put into the account each month?

$(10$ points$)$

$2$b$.$ Why did you decide on this number? Support your answer with at least $3$ sentences. $(30$ points$)$