Dustin set up an investment program using an annuity due with payments of $$615\mathrm{.}00$ at the beginning of each quarter.

a$.$ Calculate the amount of the annuity if they make payments for $13$ years into an account paying $3\mathrm{.}5\%$ compounded quarterly.

b$.$ Calculate the interest earned on Dustin's account during the $13-$year investment period.