Claude and Mike are a young couple of working professionals living in Thunder Bay, Ontario. Together, they have a combined gross monthly income of $$6,250.$ They currently pay $$280$ per month towards a lease on their car and Claude makes a payment of $$170$ per month towards her school debt. They have also developed a high credit score, by keeping their credit card balances low and paying off all bills and debts on time.

Claude and Mike have been putting money aside from each of their paycheques to save up for a down payment of $20\%$ on a $$180,000$ condo. Once they saved up enough money, they began researching different mortgage options online.

Through their research, Claude and Mike discovered that in addition to big banks, there are mortgage brokers who can assist them with their mortgage. A mortgage broker will negotiate terms with multiple different potential lenders, and as such, can often find the lowest interest rate offered by a financial lending institution. In addition to this, a mortgage broker is paid commission by the lender, and therefore, the service would not be of cost to Claude and Mike.

Intrigued by this, the couple contacted a Canadian mortgage broker company, that has access to over $30$ of the top mortgage lenders in Canada.

a$.$ What size of mortgage do the couple require?

Round to the nearest cent.

b$.$ If the mortgage broker is able to secure them with a ten$-$year mortgage with a fixed rate of $2\mathrm{.}32\%$ compounded semi$-$anually for a term of five years, what would be the size of their monthly payment?

Round to the nearest cent.

c$.$ Claude and Mike are informed that the utilities and taxes on their condo will be approximately $$190$ per month. Assuming the mortgage terms outlined in $($b$),$ calculate the GDS and TDS$.$

GDS $=$

$\%$

Round to $2$ decimal places.

TDS $=$

$\%$

Round to $2$ decimal places.

Based on the calculations, is it advisable for the lender to qualify the couple for their mortgage?

Yes

No

The couple accepted the mortgage terms, and made monthly payments for five years. At the end of the term, a new term of five years with a fixed rate of $2\mathrm{.}20\%$ compounded semi$-$anually was negotiated.

d$.$ What is the new monthly payment that Claude and Mike must make?

Round to the nearest cent.

e$.$ Instead of making monthly payments, the mortgage broker presented an option of accelerated bi$-$weekly payments, in which the couple must make a payment of half the amount calculated in $($d$)$ every two weeks. Claude and Mike opted for the accelerated bi$-$weekly payment schedule. By how many weeks did they shorten their amortization period?

weeks

Round up to the next payment and week.

f$.$ Construct a partial mortgage schedule the mortgage broker can present to the couple, showing:

the first two payments of the first term,

the last two payments of the first term,

the first two payments of the second term,

the last two payments of the second term, and,

the total payment made and interest paid.

Payment Number Amount Paid $($Periodic Payment$)$

PMT $($$$)$ Interest Portion $($Previous Balance $\backslash$times i $)$

INT $($$$)$ Principal Portion

$($PMT $-$ INT$)$ PRN $($$$)$ Principal Balance $($Previous Balance $-$ PRN$)$

BAL $($$$)$

$0---$

$1$

$2$

$...$

$58$

$59$

$60$

$61$

$62$

$...$

$$0\mathrm{.}00$

Total