show me all the calculations without excel

Question $3$: Application of Time Value of Money to Mortgages $(30$ marks$)$

Shanna wants to buy a 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 $4\mathrm{.}5\%$; this rate would be compounded semi$-$

annually, while her 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 Shanna 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 your mortgage to take advantage of the reduced interest

rate. How would her monthly payments change if she could refinance her 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$)$