You just bought a condo for $$250,000$ and paid $$50,000$ as down payment. The remaining amount is financed through a loan of $4\mathrm{.}5\%$ compounded monthly. The loan is for $15$ years. You have to make monthly payments at the end of each month. What is your monthly payment? What is the balance of this loan after ten tears? What is the total interest paid on this loan for $15$ years?