A couple borrows $\backslash (\backslash$$ $225000\backslash )$ for a mortgage that requires fixed monthly payments over $30$ consecutive years. The first monthly payment is due in one month. If the interest rate on the mortgage is $\backslash (6\mathrm{.}00\backslash \%\backslash ),$ which of the following comes closest to the monthly payment?

$\backslash (\backslash$$ $662\mathrm{.}50\backslash )$

$\backslash$$$1343\mathrm{.}70$

$\backslash$$$1348\mathrm{.}99$

$\backslash$$$625\mathrm{.}00$

$\backslash$$$1362\mathrm{.}17$