While buying a new car, Alexander made a down payment of $$1,100$ and agreed to make month$-$end payments of $$290$ for the next $5$ years and $7$ months. She was charged an interest rate of $4\%$ compounded semi$-$annually for the entire term. a$.$ What was the purchase price of the car? Round to the nearest cent b. What was the total amount of interest paid over the term?