$[6$ points total: $1$ point for each part$]$ Consider a $$1,00010-$year bond that pays a $2\mathrm{.}5\%$ annual coupon.

$($a$)$ Compute the current price and the duration $($using excel$)$ of this bond, given that the interest rate is $2\mathrm{.}5\%.$

$($b$)$ Suppose that the interest rate jumps to $3\%.$ What is the percent price change in the bond? Use the approximate formula based on Duration that we learned in class for the remainder of this problem $($b$)-($f$)$;

$($c$)$ What is the new price level of the bond?

$($d$)$ Suppose that the interest rate is $2\mathrm{.}5\%$ at $t1$ and $t2,$ but will jump at $t3$ to $3\%$ and stay at $3\%$ forever. If you are the only person that knows this information, what will be the bond price at $t1,$ at $t2$ and at $t3?$

$($e$)$ Refer to question $($d$).$ If you can invest only in either this bond or in cash $($that offers zero interest$),$ would you keep or sell the bond at $t1?$ At $t2?$

$($f$)$ Refer to question $($d$),$ but suppose that everyone in the market knows at time $t1$ that the interest rate will jump at $t3$ to $3\%.$ What will be the bond price at $t1,$ at $t2$ and at $t3?$