$6)$A company must pay liabilities of $1000$ at the end of year $1$ and X at the end of year $2.$

The only investments available are:

i$)$ One$-$year zero$-$coupon bonds with an annual effective yield of $5\%$

ii$)$ Two$-$year bonds with a par value of $1000$ and $10\%$ annual coupons, with an annual effective yield of $6\%$

The company constructed a portfolio that creates an exact cash flow matching strategy for these liabilities. The total purchase price of this portfolio is $1783\mathrm{.}76.$ Calculate the amount invested in the one$-$year zero$-$coupon bonds.