Please show step by step solutions.

Problem #$5$: A $10-$year bond has face value $($redemption value$)$ $$400,000$ and quarterly coupons of $2\mathrm{.}5\%.$ Consider the time

right after the $12$ th coupon has been paid, when the yield is $4\mathrm{.}8\%.$

$($a$)$ What is the price of the bond?

$($b$)$ Compute the price of the bond if the yield were to increase by $1$ basis point $($a basis point is $\frac{1}{100}$ of $1\%).$

What is the absolute value of the difference between that price, and your answer to part a$)?$

$($c$)$ Would the yield have to increase or decrease in order for the bond to increase in value by $$872\mathrm{.}38?$

$($d$)$ Based only on your answer to b$),$ approximately how many basis points $($bp$)$ would the yield have to move in

order for the bond to increase in value by $$872\mathrm{.}38?$

$($Answer as a positive integer.$)$

Problem $$5(a)$ :

Answer correct to $2$ decimals.

Problem #$5($b$)$:

Answer correct to $2$ decimals.

$($A$)$ Decrease $($B$)$ Increase

Problem #$5($c$)$:

Problem #$5($d$)$:

Answer as a positive integer