The following table summarizes prices of several discount bonds paying $$1$ at maturity:

Please answer the folowing sub$-$questions using information from this table.

$1-$year spot rate:

$\%$

$2-$year spot rate:

$\%$

$3-$year spot rate:

$\%$

$1-$year forward rate in year $1($the forward rate that applies to the period from year $1$ to year $2)$:

$\%$

Now suppose the $1-$year spot rate is $r_1=1\mathrm{.}1\%,$ the $2-$year spot rate is $r_2=2\%,$ and the $1-$year forward rate in year $1$

is $f_1=4\mathrm{.}4\%.$ The prices of bonds are different from the subquestions above.

Assume at time $0$ we invest $$x$ in $1-$year bond, short $$x$ in $2-$year bond, and invest $$y$ at time $1$ at the fixed forward rate.

If this is an arbitrage strategy generating $$100$ at time $t=1$ and nothing otherwise, then:

$x=$

$y=$

Note that since we effectively borrow $y,y$ is a negative number.