Your friend tells you he has a very simple trick for taking​ one-third of the time it takes to repay your​ mortgage: Use your Christmas bonus to make an extra payment on January 1 of each year​ (that is, pay your monthly payment due on that day​ twice). Assume that the mortgage has an original term of years and has an APR of . a. If you take out your mortgage on January 1​ (so that your first payment is due on February​ 1), and you make your first extra payment at the end of the first​ year, in what year will you finish repaying your​ mortgage? b. If you take out your mortgage on July 1​ (so that the first payment is on August​ 1), and you make the extra payment each​ January, in how many months will you pay off your​ mortgage? c. How will the amount of time it takes to pay off the loan given this strategy vary with the interest rate on the​ loan?