The $1-$year risk$-$free interest rate of investments in US dollars is $r_{\text{U}\text{S}\text{D}}=1\mathrm{.}22\%.$ The $1-$year risk$-$

free interest rate of investments in Canadian dollars is $r_{\text{C}\text{A}\text{D}}=4\mathrm{.}0\%.$ The current $($spot$)$ exchange

rate between the two currencies is $1\mathrm{.}41$ : the price of $1$ USD is $1\mathrm{.}41$ CAD. The $1-$year forward price

of $1$ USD is $1\mathrm{.}41$ CAD. You can trade in $1-$year risk$-$free discount bonds denominated in both US and

Canadian dollars in the forward contract to buy $1$ USD $1$ year from now, and in the spot foreign

exchange market, where you can buy and sell USD.

Consider the following strategy:

Borrow $x$ USD at $1\mathrm{.}22\%$ today, which means that the total loan repayment obligation after a

year would be $(1+1\mathrm{.}22\%)x$ USD.

Convert $y$ USD into CAD at the spot rate of $1\mathrm{.}41.$

Lock in the $4\mathrm{.}0\%$ rate on the deposit amount of $1\mathrm{.}41y$ CAD, and simultaneously enter into a

forward contract that converts the full maturity amount of the deposit into USD at the one$-$

year forward rate of USD $=1\mathrm{.}41$ CAD.

After one year, settle the forward contract at the contracted rate of $1\mathrm{.}41.$ Suppose the

above arbitrage strategy generates $100$ USD today and nothing otherwise, please solve for

$x$ and $y.$

$x=$

$y=$