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
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:
A: 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.)
B: 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
Malcolm and Shannon agreed to look at their options before giving the loans officer
their final decision.
1. 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?
2. Suppose the couple choose to refinance 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 Malcolm and Shannon have to pay in this situation?
3. 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?
4. If the penalty amount is added to the principal when the mortgage is renegotiated,
what will the new monthly payment be?
Case Study Planning for University
▶ Victor and Jasmine Gonzalez were discussing how to plan for their three young
sons’ university education. Stephen turned 12-years old in April, Jack turned 9 in
January, and Danny turned 7 in March. Although university was still a long way off
for the boys, Victor and Jasmine wanted to ensure enough funds were available for
Victor and Jasmine decided to provide each son with a monthly allowance that would
cover tuition and some living expenses. Because they were uncertain about the boys’
finding summer jobs in the future, Victor and Jasmine decided their sons would
receive the allowance at the beginning of each month for four years. The parents also
assumed that the costs of education would continue to increase.
Stephen would receive an allowance of $1000 per month starting September 1 of the
year he turns 18.
Jack would receive an allowance that is 8% more than Stephen’s allowance. He
would also receive it at the beginning of September 1 of the year he turns 18.
Danny would receive an allowance that is 10% more than Jack’s at the beginning of
September of the year he turns 18.
Victor and Jasmine visited their local bank manager to fund the investment that would
pay for the boys’ allowances for university. The bank manager suggested an
investment paying interest of 4.0% compounded monthly, from now until the three
boys had each completed their four years of education. Victor and Jasmine thought
this sounded reasonable. So on June 1, a week after talking with the bank manager,
they deposited the sum of money necessary to finance their sons’ post-secondary
1. How much allowance will each of the boys receive per month based on their
parents’ assumptions of price increases?
2.(a) How much money must Victor and Jasmine invest for each son on June 1 to
provide them the desired allowance?
(b) Create a timeline of events for each of the sons.
(c) What is the total amount invested on June 1?
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