Case Study $1$

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

Scenario

Two years ago, Yuki and Thea purchased their first home for a purchase price of $$696,800,$ which they paid with a $$69,300$ down payment

and a $$627,500$ mortgage. At that time, Yuki and Thea both had student loans and needed to borrow money from their parents to fund most

of the down payment.

Yuki's parents lent them $$15,500$ at $0\%$ interest, with the expectation that the loan be paid back in five annual payments of $$3,100,$ made at

the end of each year. Thea's parents lent them $$23,500$ at $2\mathrm{.}5\%$ simple interest. They agreed that Yuki and Thea would make payments of

$$4,700$ plus interest at the end of each year for five years, with the first payment due two years from the date of the loan.

The purchase of the house was a good decision. As a result of a strong real estate market, Yuki and Thea now have $$130,000$ of equity in

their house. Unfortunately, after purchasing the house, Yuki and Thea made some poor financial decisions that resulted in substantial credit

card debt. This included using their credit cards to make purchases that they could not afford and using cash advances to make payments on

their various loans.

A summary of Yuki and Thea's loans and credit card debts as of the first day of year $3$ since the house purchase is shown in the table below.

All interest rates are simple interest.

As Yuki and Thea are at ends trying to pay their bills, they reach out to their local not$-$for$-$profit credit counselling society for help. After

reviewing Yuki and Thea's case, their credit counsellor proposes the following course of action:

Leverage the equity in Yuki and Thea's home to obtain a home equity line of credit $($HELOC$).$ The credit counsellor can help Yuki and

Thea acquire a HELOC with payments of $$300$ plus interest per month, with a simple interest rate of prime $+3\%.$

Use the HELOC to pay off the credit card balances and loans that carry a higher interest rate than the HELOC and close the

associated accounts so no further debt can be accrued.

Convert all remaining loans to a monthly payment schedule.

Tasks

As an intern working for the credit counselling society, you've been tasked with working out the details for Yuki and Thea's debt consolidation

plan, which you will then present in a written report. Your tasks are as follows:

Find and report the current Bank of Canada prime rate, including the date and the source you used. $(5$ marks$)$

Calculate the equivalent payment that would be necessary to pay off the loans from Yuki and Thea's parents if the loans were to be

paid off today using the HELOC. Also, calculate the monthly payments on each of the loans from Yuki and Thea's parents, given that

the loans are paid back with monthly payments over the original time frames of the loans. $(5$ marks$)$

For each student loan and credit card balance, calculate the current monthly payments and interest charges on the debts. $(5$ marks

for each student loan and credit card; total: $30$ marks$)$

For each student loan and credit card balance, calculate the monthly payments and interest charges on the debt that would result

from using the HELOC to pay off the current balance. $(5$ marks for each loan and credit card; total: $30$ marks$)$