Homework due Aug $1,202402$:$12$ CDT

Question $3$

$\frac{0\mathrm{.}0}{20\mathrm{.}0}$ points $($graded$)$

The $1-$year risk$-$free interest rate of investments in US dollars is $r_{\text{U}\text{S}\text{D}}=1\mathrm{.}1\%.$ The $1-$year risk$-$free interest rate of investments in Canadian dollars is $r_{\text{C}\text{A}\text{D}}=3\mathrm{.}7\%.$ The current $($spot$)$ exchange rate between the two currencies is $1\mathrm{.}47$: the price of $1$ USD is $1\mathrm{.}47$ CAD. The $1-$year forward price of $1$ USD is $1\mathrm{.}41$ CAD. You can trade in $1-$year riskfree 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 $1\mathrm{.}1\%$ today, which means that the total loan repayment obligation after a year would be $(1+1\mathrm{.}1\%)x$ USD.

Convert $y$ USD into CAD at the spot rate of $1\mathrm{.}47.$

Lock in the $3\mathrm{.}7\%$ rate on the deposit amount of $1\mathrm{.}47y$ 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 $y.$

$x=$

$y=$