Sarah is $30$ years old and will retire in $35$ years and wishes to save up enough money so she can withdraw $$20,000$ per month for $20$ years starting one more after she retires. Her RRSP account earns $9\%$ interest compounded semi$-$annually when she retires she will convert her RRSP to an RRIF which will earn $7\%$ interest per year compounded monthly.

She plans on saving money every month between now and retirement.

a$.$ How much should she save each month?