$S_1$ is a stock with price $30$ and quarterly dividends of $0\mathrm{.}25.$ The next dividend is payable in $3$ months.

$S_2$ is a nondividend paying stock with price $40.$

The continuously compounded risk$-$free interest rate is $5\%.$

Let $x$ be the premium of an option to give $S_1$ in exchange for receiving $S_2$ at the end of $6$ months, and let $y$ be the premium of an option to give $S_2$ in exchange for receiving $S_1$ at the end of $6$ months.

Determine $x-y.$