A $$1,000$ face value bond of Acme Inc. pays an annual coupon and carries a coupon

rate of $8\mathrm{.}25\%.$ It was a $30$ year bond when issued and it has $11$ years remaining to

maturity. If it currently has a yield to maturity of $7\mathrm{.}75\%.$

$($a$)$ What interest payments do bondholders receive each year?

$($b$)$ What is the current bond price?

$($c$)$ What is the bond price if the yield to maturity rises to $8\mathrm{.}625\%?$