Suppose your parents wish to buy a house whose current market value is $$150,000.$ They have approached a loan officer at the Bank of Nova Scotia who offers them $25-$year mortgage financing for $75\%$ of the purchase price at an annual rate of $6\mathrm{.}75\%.$ Payments are to be made on a monthly basis even though the bank is required by Canadian laws to compound the interest semi$-$annually.

$($a$)$ What are the effective annual and monthly rates of interest on the loan?

$($b$)$ Assuming the loan payments are due at the end of each month:

$($i$)$ determine the amount of the monthly loan payments

$($ii$)$ determine the amortization schedule for the first $3$ months

$($iii$)$ determine the principal outstanding at the end of the $5$th year. How much interest

has been paid over the $5$ years?