Given data: Year $1$ YTM $5\%,$Year $2$ YTM $5\mathrm{.}25\%,$ Year $3$ YTM $5\mathrm{.}75\%,$ Year $4$ YTM $6\%,$ Year $5$ YTM $6\mathrm{.}20\%,$ Year $6$ YTM $6\mathrm{.}40\%,$Year $7$ YTM $6\mathrm{.}80\%,$ Year $8$ YTM $7\%,$ Year $9$ YTM $7\mathrm{.}30\%,$ Year $10$ YTM $7\mathrm{.}80\%$

Given data: Year $1$ liquidity premium $0\%,$ Year $2$ liquidity premiuim $0\mathrm{.}10\%,$ Year $3$ liquidity premium $0\mathrm{.}20\%,$ Year $4$ liquidity premium $0\mathrm{.}30\%,$ Year $5$ liqudity premium $0\mathrm{.}40\%,$ Year $6$ liquidity premium $0\mathrm{.}50\%,$ Year $7$ liquidity premium $0\mathrm{.}60\%,$ Year $8$ liquidity premium $0\mathrm{.}70\%,$ Year $9$ liquidity premium $0\mathrm{.}80\%,$ Year $10$ liquidity premium $0\mathrm{.}90\%$

$1.$ Calculate the expected one year interest rates under the expectations theory.