When Monica retires in $13$ years, he wants to receive $$1,000\mathrm{.}00$ payments at the start of every month for $27$ years from his RIF that earns $2\mathrm{.}50\%$ compounded semi$-$annually.

a$.$ What must the balance be in Monica$$s RIF in order to sustain the $$1,000\mathrm{.}00$ payments?

Round to the nearest cent

b$.$ What beginning of quarter deposits does Monica have to make into his RRSP that earns $2\mathrm{.}90\%$ compounded quarterly for the $13$ years until he retires?