A home buyer borrows $225,000$ and has two options to repay the loan, both at an annual nominal interest rate of $i,$ convertible monthly:

Option $1$: Level payments of $1960$ at the end of each month for $180$ months.

Option $2$: Level payments of $x$ at the beginning of each month for $360$ months.

Calculate $x.$

$1415$

$1418$

$1422$

$1427$

$1435$