Question $4$: Application of Time Value of Money to Mortgages $(30$ marks$)$ Abigail graduated from Carleton University $5$ years ago and has been working since then. She wants to buy her first house costing $$325,000$ and has obtained a loan from TD Bank. A minimum down payment of $15\%$ would be required and the bank will provide the difference. Her grandparent have told her that they will cover her down payment.

a$.$ TD Bank has quoted her mortgage interest rate is $4\mathrm{.}5\%.$ By Canadian laws, this rate would be compounded semi$-$annually, while her mortgage payments would be made monthly. What is the effective monthly interest rate $($EMR$)$ that she would pay? $(5$ marks$)$

b$.$ Calculate her monthly mortgage payment, assuming $15\%$ down payment from her grandparents and a mortgage maturity of $25$ years. $(5$ marks$)$

c$.$ Given $($b$)$ above, how much of her payment in the $2$nd month will go toward repayment of principal and how much is interest payment? $(5$ marks$)$

d$.$ Assuming that five years later, interest rates drop to $3\mathrm{.}2\%$ and Abigail decides to refinance the mortgage. How much would she have paid in interest and how much of the original loan have you paid over the five years? $(5$ marks$)$

e$.$ Suppose she decides to refinance her mortgage to take advantage of the reduced interest rate. How would her monthly payments change if she could refinance the mortgage at $3\mathrm{.}2\%($with a $20-$year term loan$)?(5$ marks$)$

f$.$ Suppose she kept her monthly payments at the original amount found in $($b$)$ above at $4\mathrm{.}5\%,$ but refinanced the at $3\mathrm{.}2\%,$ how long would it take her to pay off the mortgage? $(5$ marks$).$