$1.$Keys Corporation's $5-$year bonds yield $6\mathrm{.}50\%,$ and $5-$year T$-$bonds yield $4\mathrm{.}40\%.$ The real risk$-$free rate is r$*=2\mathrm{.}5\%,$ the liquidity premium for Keys' bonds is LP $=0\mathrm{.}5\%$ versus zero for T$-$bonds, and the maturity risk premium for all bonds is found with the formula MRP $=($t $1)*0\mathrm{.}1\%,$ where t $=$ number of years to maturity. Answer the following questions:

$(1)$ What is the inflation premium $($IP$)$ for $5-$year bonds? $(1\mathrm{.}25$ points$)$

$(2)$ What is the default risk premium $($DRP$)$ on Keys' bonds? $(1\mathrm{.}25$ points$)$

$2.$ For each selected day, compare the nominal and real yields at the following $5$ maturities: $5$ years, $7$ years, $10$ years, $20$ years, and $30$ years.

A$.$ Based on the formula rnominal $=$ rreal $+$ i$,$ calculate the rates of inflation on these five days at the abovementioned maturities. $(1\mathrm{.}25$ points$)$

Note: Only the abovementioned maturities are considered for real yield curves.

B$.$ Draw the daily inflation rate curves $($five curves$)$ on a scatter plot. $(1\mathrm{.}25$ points$)$