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

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:

Mahmoud$$s parents$-$ current bal: $$15,600$ @ $0\%$ simple int Yearly pymt $$5,200$

James$$s parents$-$ current bal: $$18,800$ @ $3\mathrm{.}5\%$ simple int Yearly pymt $$4,700$

Mahmoud$$s student loan$-$ current bal: $$7,500$ Prime $7\mathrm{.}20\%+3\%$ Monthly Pymt $$200$

James$$s student loan$-$ current bal: $$11,500$ Prime $7\mathrm{.}20\%+3\%$ Monthly Pymt $$200$

Credit card $1-$ current bal: $$6,50027\%$ Simple Min $5\%$ of balance plus int per month

Credit card $2-$ current bal:$$13,50018\%$ Simple Min $3\%$ of balance plus int per month

Credit card $3-$ current bal:$$10,00018\%$ simple Min $3\%$ of balance plus int per month

Credit card $4-$ current bal:$$3,0002\%$ simple $$200$ plus interest per month

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

$2.$ 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$)$

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

$7.$ Determine the change in Mahmoud and James$$s total payment over the next twelve months as a result of the debt consolidation. $(5$ marks$)$

$8.$ Determine how much total interest is saved over the next twelve months as a result of the debt consolidation. $(5$ marks$)$

$9.$ Determine the change in the average interest rate Mahmoud and James would pay before and after they consolidate their debts. $(5$ marks$)$