2. A home loan package offers a fixed 2.4% p.a. compounded monthly for the first 5 years, and after 5 years the interest rate increases to 4.2% p.a. compounded monthly. A loan of $300,000 is taken out with level repayments of $1,986.28 per month at the end of each month for the life of the loan. Determine how long it takes to pay off this loan. (a) Suppose the loan had been at a fixed interest rate of 2.4% p.a. compounded monthly for the lifetime of the loan. Calculate how long it would take to pay off the loan. Give your answer rounded to the nearest month. (b) Use your answer to (a) to calculate the unpaid balance of the loan after 5 years. Give your answer rounded to the nearest cent. (c) Use your answer to (b) to calculate how long it will take to pay off the remainder of the loan at the higher interest rate. Give your answer rounded to the nearest month. (d) How long does it take to pay off the loan