A $10-$year bond has face value $($redemption value$)$ $$650,000$ and quarterly coupons of $1\mathrm{.}5\%.$ Consider the time right after the $12$th coupon has been paid, when the yield is $3\mathrm{.}7\%.$

$($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 $1/100$ 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 $$2950\mathrm{.}92?$

$($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 $$2950\mathrm{.}92?$

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