This question is not cumulative

$[10$ marks$]$

$($a$)$ The current market wide interest rate is $7$ percent. The price of a $6$year coupon bond with $$1,000$ par value, semi$-$annual coupon payments, is $$830\mathrm{.}89.$ How much is the coupon rate of this bond?

$($b$)$ Watters Umbrella Corp. issued $12-$year bonds $2$ years ago at a coupon rate of $7\mathrm{.}8$ percent. The bonds make semiannual payments. If these bonds currently sell for $105$ percent of par value, what is the YTM$?($Write down the expression for YTM and then use a financial calculator or a spreadsheet program to find the answer$)$

$($c$)$ Three years ago, an investor bought a $15-$year zero$-$coupon bond with a $$1,000$ par value and $8$ percent yield to maturity. Today, the market interest rates are $6\mathrm{.}5$ percent. What is the price of this bond now? How much money has the investor gained$/$lost$?$ What is her annual holding period return?