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8/15/25 – 7:59:50 AM MDT

Name:

____________________________

Class:

MATH244R10 Business Mathematics – Section 4

Class #:

____________________________

Section #:

____________________________

Instructor:

Ryan Tifenbach

Assignment:

Case Study 2

Question 1: (75 points)

Case Study 2

To complete the case study, read the scenario, then complete the tasks that follow it.

Scenario

Working as a financial adviser, you’ve just been assigned a new client. Hannah just turned 28 and is seeking advice on retirement planning.

Hannah expects to retire at the age of 65 and will convert her registered retirement savings plan (RRSP) into a retirement income fund (RIF) and begin withdrawing money from her RIF at that time. Under her current savings plan, she is contributing $450 a month until she retires into an RRSP that is expected to earn 6% compounded monthly. Beginning one month after her 65th birthday, Hannah plans on withdrawing monthly from the RIF, which she expects will earn a more conservative 5% compounded monthly. She plans to spread the payments over 20 years.

Hannah also purchased a house at the age of 24. At that time, she signed a 5-year term mortgage for $350,000 at a rate of 4.75% compounded semi-annually and amortized over 25 years, with monthly payments. In one year’s time, Hannah will need to renew her mortgage.

Hannah’s objective is to maximize her retirement savings. Having done some research on the huge interest costs involved with mortgages, she knows that some mortgages offer an accelerated option that allows the mortgagee to pay off the mortgage faster by making additional payments that are applied directly against the principal. As such, Hannah is seeking your advice on whether she should

a. continue with her current contributions to her RRSP and renew her mortgage on the current 25-year amortization schedule or

b. pause her contributions to her RRSP, diverting those funds to paying down her mortgage at a faster rate.

She has flexibility to increase her monthly payments to her mortgage but is also wary of a loss of disposable income.

Hannah has spoken with a mortgage broker as well and is considering three options:

Option 1: Continue with the current course of action. The details are as follows:

· Until she retires, Hannah contributes $450 a month into an RRSP expected to earn 6% compounded monthly.

· She maintains the 25-year amortization period and renews her mortgage for four successive 5-year terms at a rate of 4.75% compounded semi-annually and amortized over 25 years.

Option 2: Renew the mortgage without the accelerated payment option but increase the amount of the mortgage payments to pay off the mortgage in a total of 15 years (i.e., 10 years from the renewal date). Continue with the current contributions to the RRSP. The details are as follows:

· Hannah renews the mortgage with increased payments to reduce the amortization period from 25 years to 15 years. The mortgage broker is offering a 5-year term at 8% compounded semi-annually, amortized over 15 years, with bi-weekly payments, followed by a 5-year term at 8.5% compounded semi-annually, amortized over 15 years, with weekly payments.

· Until she retires, Hannah contributes $450 a month into an RRSP expected to earn 6% compounded monthly.

Option 3: Renew the mortgage with the accelerated payment option. Increase the amount of the regular mortgage payments to pay off the mortgage in a total of 15 years (i.e., 10 years from the renewal date) and divert contributions from the RRSP to the mortgage until the mortgage is paid off. Resume payments to the RRSP after the mortgage is paid off. The details are as follows:

· Hannah renews the mortgage with increased payments to reduce the amortization period from 25 years to 15 years. The mortgage broker is offering a 5-year term at 8.25% compounded semi-annually, amortized over 15 years, with bi-weekly payments, followed by a 5-year term at 8.75% compounded semi-annually, amortized over 15 years, with weekly payments.

· She ceases contributing $450 a month to the RRSP until her mortgage is paid off. Instead, she adds this $450 per month payment to her mortgage payment as an accelerated payment, which is split evenly over her biweekly and then weekly payments. The accelerated payments are applied directly to the mortgage’s principal. (
Note: To track the impact of the accelerated payments, you must complete a full amortization schedule for all three terms. This will also allow you to determine when her mortgage will be paid off.)

· Hannah resumes contributions to the RRSP once her mortgage is paid off. Until she is 65, she takes the last monthly amount she was paying on her mortgage and pays it into the RRSP monthly instead.

Tasks

Evaluate the three options outlined above and prepare a brief report (written in MS Word) for Hannah. Your report should include

a. an explanation of the rationale for each option that outlines the pros and cons associated with each. 
(5 marks for each option; total: 15 marks)

b. a table comparing the three options. The table should include the following information for each option: the monthly mortgage payment, monthly RRSP contribution, total monthly payments to the RRSP and mortgage, total amount paid on the mortgage, total interest paid on the mortgage, total value of the RRSP at retirement, and expected monthly payment from the RIF. 
(20 marks for the calculations associated with the mortgage, 15 marks for the RRSP calculations, and 10 marks for the RIF calculations; total: 45 marks)

c. a summary detailing your recommendation as to the best of the three options provided for Hannah based on her objective of maximizing her retirement funds. In addition, suggest an alternative option that Hannah hasn’t considered. You do not need to analyze this option, but should explain why you think this might be a better alternative. 
(15 marks)

Total: 75 marks

Your report should include all supporting calculations in an appendix. Show the details of all calculations to ensure partial grades can be awarded for your work.

When you have completed it, upload your report (including appendix) into the box below.

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