Please solve parts c$-$f from the question below.

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

$($d$)$ Suppose that the interest rate is $2\mathrm{.}5\%$ at $t+1$ and $t+2,$ but will jump at $t+3$ to $3\%$ and stay at $3\%$ forever. If you are the oenly person that knows this information, what will be the bond price at $t+1,$ at $t+2$ and at $t+3?$

$($e$)$ Refer to question $($d$).$ If you can invest only in either this bood or in cash $($that offers zero interest$),$ would you keep or sell the bond at $t+1?$ At $t+2?$

$($f$)$ Refer to question $($d$),$ but suppose that everyone in the market knows at time t$+1$ that the inferest rate will jump at $t+3$ to $3\%.$ What will be the bood price at $t+1,$ at $t+2$ and at $t+3?$