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 amortized over 25 years. Payments were made monthly.

After 3 years, interest rates had fallen significantly. In response, Malcolm and Shannon considered paying out the old mortgage (in spite of the interest penalties), and negotiating 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. According to their mortgage contract, the penalty for renegotiating the mortgage before the end of the 5-year term is the greater of:

Three months' interest at the original rate of interest. (Banks generally calculate this as one month's interest on the mortgage principal remaining to be paid, multiplied by three.)

The interest differential over the remainder of the original term. (Banks generally calculate this as the difference between the interest the bank would have earned over the remainder of the original term at the original [higher] mortgage rate and at the renegotiated [lower] mortgage rate.)

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.

Questions

Suppose there was no penalty for refinancing the mortgage after 3 years. How much would Malcolm and Shannon save per month by refinancing their mortgage for a 5-year term at the new rate?

Suppose the couple choose to refinance their mortgage for a 5-year term at the new interest rate.

What is the amount of penalty A?

What is the amount of penalty B?

What penalty would Malcolm and Shannon have to pay in this situation?

If they pay the full amount of the penalty at the beginning of the new 5-year term, what will Malcolm and Shannon's new monthly payment be?

If the penalty amount is added to the principal when the mortgage is renegotiated, what will the new monthly payment be?

S. A. Hummelbrunner, Kelly Halliday, Ali R. Hassanlou, K. Suzanne Coombs. (2016). Contemporary Business Mathematics with Canadian Applications (11th Canadian Edition) [Texidium version]. Retrieved from http://texidium.com