Sam and Ella have just bought a home. They take out a $250,000 mortgage and have decided that they can afford $1650 a month as the mortgage payment. Here are the interest rates that Sam and Ella have been able to obtain over the years (we will assume this is a USA mortgage, so that interest rates compounded monthly are allowed; that will make the calculations a bit easier for you):

j12 = 6% Locked in for 5 years

j12 = 5.4% Locked in for 3 years

j12 = 4.8% Locked in for 5 years

After exactly 10 years of monthly payments, Sam and Ella realize that mortgage rates have dropped again and they wish to finance their mortgage.

(a) Calculate the outstanding balance after 10 years using the retrospective method. (4 marks)

For the last 3 questions, you will need your answer from (a). If you are unable to get the answer, or are not confident in your answer, you can use $170,000 as the outstanding balance.

(b) How many more $1650 monthly payments are required to fully pay off the mortgage at the rate of interest that is in effect at this time? What would be the size of the drop payment needed one month later to fully pay off the mortgage? (3 + 1 = 4 marks)

(c) Since Sam and Ella are wishing to refinance their mortgage before the end of the current 5 year locked in period, the mortgage company will charge them a penalty. The penalty is equal to 3 times one months interest on the current outstanding balance. What is the size of the penalty? (1 mark)

(d) Calculate what the mortgage interest rate, j2, has to drop to in order for it to be beneficial for Sam and Ella to refinance. Make sure you take into consideration the penalty. Assume that Sam and Ella will continue making monthly payments of $1650. For the term remaining, use you answer to (b), rounded to the nearest month. (4 marks)