Tara invested his savings into a Registered Retirement Savings Plan $($RRSP$)$ at an interest rate of $3\mathrm{.}75\%$ compounded semi$-$annually. After one year, his investment grew to $$24,600$; however, the interest rate on the RRSP changed to $4\mathrm{.}00\%$ compounded quarterly and remained constant for the next two years.

a$.$ Calculate the original amount he invested into the RRSP$.$

$

$$0\mathrm{.}00$

Round to the nearest cent

b$.$ Calculate the accumulated value of the investment at the end of three years $($two years after the rate change$).$

$

$$0\mathrm{.}00$

Round to the nearest cent