assume we have a $500,000$ mortgage at $7\%$ original interest rate, with a $30-$year term and monthly payments. The interest rate is adjusted at the end of each year, and we assume the rate increases $0\mathrm{.}5\%$ after the first year and another $0\mathrm{.}5\%$ after the second year. What is the unpaid mortgage at the end of the second year?