A real estate speculator purchases a tract of land for $$1\mathrm{.}1$ million and assumes a $25-$year mortgage at $12\%$ interest compounded monthly. $($a$)$ What is his monthly payment? $($b$)$ Suppose that at the end of $5$ years the mortgage is changed to a $10-$year term for the remaining balance. What is the new monthly payment? $($c$)$ Suppose that after $5$ more years, the mortgage is required to be repaid in full. How much will then be due?