You just celebrated your $30$th birthday and plan to retire when you turn $64.$ You have $$15,568$ accumulated in your RRSP and plan to deposit additional money each month to your RRSP for $34$ years, starting today. On your $64$th birthday you plan to withdraw $$45,000$ to pay off your mortgage and the remaining funds will be used to buy an annuity that will pay you $$4,000/$month for $26$ years, with the first withdrawal starting one month after your $64$th birthday. You anticipate earning $6\mathrm{.}5\%,$ compounded monthly, the entire time.

$($A$)$How much must you deposit each month into your retirement plan?

$($B$)$How much interest did you earn over the entire $60$ years?

$($C$)$Suppose instead of withdrawing $$45,000$ when you turn $64,$ you deposit $$41,000$ from a retirement bonus you will get when you retire. How much must you deposit each month?

$*$Shown via BAII Plus calculator steps