QUESTION-2

Case Study Managing a Mortgage Malcolm and Shannon purchased their first house with a $180 000 mortgage. Their 5- year mortgage had a 7.5% semi-annually compounded interest rate, and was amor- tized over 25 years. Payments were made monthly After 3 years, interest rates had fallen signifi- cantly. In response, Malcolm and Shannon considered paying out the old mortgage (in spite of the interest penalties), and negotiat- ing a new mortgage at the lower rate. They met with the loans officer at their bank, who laid out their options for them. Interest on mortgages with a 5-year term was 5.5% compounded semi-annually, the lowest rate in many years. The loan officer informed Malcolm and Shannon of the penalty for renegotiating a mortgage early. before the end of the current term. Accord- ing to their mortgage contract, the penalty for renegotiating the mortgage before the end of the 5-year term is the greater of A. Three months' interest at the origi- nal rate of interest. (Banks generally calculate this as one month's interest on the mortgage principal remaining to be paid, multiplied by three.) B. The interest differential over the re- mainder of the original term. (Banks generally calculate this as the differ- ence between the interest the bank would have earned over the remain- der of the original term at the origi- nal (higher) mortgage rate and at the renegotiated (lower] mortgage rate.) 3 The loans officer also explained that there are two options for paying the penalty amount: (1) you can pay the full amount of the penalty at the beginning of the new mortgage period, or (2) the penalty amount can be added to the principal when the mortgage is renegotiated, allowing the penalty to be paid off over the term of the new mortgage. Malcolm and Shannon agreed to look at their options before giving the loans officer their final decision. 2. Suppose the couple choose to refi- nance their mortgage for a 5-year term at the new interest rate. a. What is the amount of penalty A? b. What is the amount of penalty B? c. What penalty would Mal- colm and Shannon have to pay in this situation