Future Shop has a plan where you don't begin payments for $13$ months. You then begin payments of $$322$ at the beginning of every month for $18$ months. Assume the interest rate is $5\%$ compounded semiannually over the whole time interval $($even when you don't have any payments$).$ What was the value of the home theatre set at the time of purchase?The value of the home theatre set at the time of purchase was $