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:

1. 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.)
2. 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.)