Scenario

Two years ago, Mahmoud and James purchased their first home for a purchase price of $$664,400,$ which they paid with a $$67,200$ down payment and a $$597,200$ mortgage. At that time, Mahmoud and James both had student loans and needed to borrow money from their parents to fund most of the down payment.

Mahmoud$$s parents lent them $$26,000$ at $0\%$ interest, with the expectation that the loan be paid back in five annual payments of $$5,200,$ made at the end of each year. James$$s parents lent them $$23,500$ at $3\mathrm{.}5\%$ simple interest. They agreed that Mahmoud and James would make payments of $$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, Mahmoud and James now have $$135,000$ of equity in their house. Unfortunately, after purchasing the house, Mahmoud and James 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.

Debt Current Balance Simple Interest Rate on Debt Monthly Payment Yearly Payment

Mahmoud$$s parents $$15,6000\%$ $$5,200$

James$$s parents $$18,8003\mathrm{.}5\%$ $$4,700$

Mahmoud$$s student loan $$7,500$ Prime $7\mathrm{.}20+3\%$ $$200$

James$$s student loan $$11,500$ Prime $7\mathrm{.}20+3\%$ $$200$

Credit card $1$ $$6,50027\%$ Minimum $5\%$ of balance plus interest

Credit card $2$ $$13,50018\%$ Minimum $3\%$ of balance plus interest

Credit card $3$ $$10,00018\%$ Minimum $3\%$ of balance plus interest

Credit card $4$ $$3,0002\%$ $$200$ plus interest

A summary of Mahmoud and James$$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 Mahmoud and James are at ends trying to pay their bills, they reach out to their local not$-$for$-$profit credit counselling society for help. After reviewing Mahmoud and James$$s case, their credit counsellor proposes the following course of action:Debt Current Balance Simple Interest Rate on Debt Monthly Payment Yearly Payment

Mahmoud$$s parents remaining $$15,6000\%$ $$5,200$ yearly

James$$s parents remaining $$18,8003\mathrm{.}5\%$ $$4,700$ yearly

Mahmoud$$s student loan $$7,500$ Prime $7\mathrm{.}20+3\%$ $$200$ monthly

James$$s student loan $$11,500$ Prime $7\mathrm{.}20+3\%$ $$200$ monthly

Credit card $1$ $$6,50027\%$ Minimum $5\%$ of balance plus interest monthly

Credit card $2$ $$13,50018\%$ Minimum $3\%$ of balance plus interest monthly

Credit card $3$ $$10,00018\%$ Minimum $3\%$ of balance plus in$2.$ Calculate the equivalent payment that would be necessary to pay off the loans from Mahmoud and James$$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 Mahmoud and James$$s parents, given that the loans are paid back with monthly payments over the original time frames of the loans. $(5$ marks$)$

$3.$ 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$)$

$4.$ 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$)$

$6.$ Determine the change in Mahmoud and James$$s total monthly payment as a result of the debt consolidation. $(5$ marks$)$