$1.$ Ironwood Bank is offering a $30-$year mortgage with an APR of $6\mathrm{.}05\%$ based on monthly compounding. If you plan to borrow $$164000,$ what will be your monthly payment?$($ Note: Be careful not to round any intermediate steps less than six decimal places.$)$

$2.$ You have decided to refinance your mortgage. You plan to borrow whatever is outstanding on your current mortgage. The current monthly payment is $ $2435\mathrm{.}32$ and you have made every payment on time. The original term of the mortgage was $30$ years, and the mortgage is exactly four years and eight months old. You have just made your monthly payment. The mortgage interest rate is $6\mathrm{.}125\%($APR$).$ How much do you owe on the mortgage today? $($Note: Be careful not to round any intermediate steps less than six decimal places.$)$

$3.$ You have invested in a business that proudly reports that it is profitable. Your investment of $$5000$ has produced a profit of $ $300.$ The managers think that if you leave your $ $5000$ invested with them, they should be able to generate $$300$ per year in profits for you in perpetuity. Evaluating other investment opportunities, you note that other long$-$term investments of similar risk offer an expected return of $8\mathrm{.}00\%.$ Should you remain invested in this firm?