Question $22(11$ marks$)$

The Harveys are purchasing a home for $$12,500,000$ and have made the required deposit of $12\%$ and have also paid the closing cost of $$1,000,000.$ They have been pre$-$approved by County Building Society to qualify for a $25-$year mortgage loan for the balance to close the purchase. This will attract an interest rate of $5\mathrm{.}50\%$ per annum with monthly compounding.

$($a$)$ Use a full amortisation table to show what the loan balance would be at the end of the first three months on the Harveys' new mortgage loan.

$(5$ Marks$)$

$($b$)$ If the Harveys are planning to make only the required monthly payments on the loan and then use a lumpsum deposit to pay off their mortgage at the end fifteen years, what would be the total interest payable over the period?