$$Mortgage amortization$$

Mrs$.$ and Mr$.$ Hill purchased a detached home in North York for $$1,200,000\mathrm{.}00$ with a down payment of $25\%.$ For the remainder they signed a mortgage contract with BMO at $6\mathrm{.}25\%$ compounded semi$-$annually $($ fixed rate for $5$ years$)$ and monthly payments for $25$ years.

Find the regular monthly payment and the smaller final payment.$[2$ marks$]$

b$.$ Find the total interest $($total cost of financing$).[1$ mark$]$

c$.$ Show the first three lines of the amortization schedule.$[2$ marks$]$

d$.$ Find the outstanding balance after $3$ years. $[1$mark$]$

e$.$ Find the total principal and the total interest paid in the first $3$ years. $[2$marks$]$

f$.$ Calculate their equity after three years $[2$mark$]$

g Suppose they decided to pay an extra $10\%$ of the original mortgage loan after $3$ years. How much interest would this save over the life of the mortgage? $[3$marks$]$

h$)$ After $3\mathrm{.}5$ years, interest rates drop to $4\mathrm{.}52\%$ compounded semi$-$annually. There is a penalty of $3$ months$$ interest on the outstanding balance for early repayment. Does it pay to refinance? $[3$marks$]$

i$).$ If the penalty is based on the interest rate differential $($difference between the contractual interest rate on the loan and the current interest rate$),$ calculated as :

Penalty $=($outstanding loan balance$)\backslash$times IRD $\backslash$times $($term remaining in payment periods$)$

Does it pay to refinance? $[3$marks$]$