You have just purchased a home and taken out a $$500,000$ mortgage. The mortgage has a $30-$

year term with monthly payments and an APR $($with semi$-$annual compounding$)$ of $6\mathrm{.}5\%.$

Calculate the monthly mortgage payment and complete the amortization schedule for the first $5$

months. Show all calculations to support your answer. $(25$ points$)$