Questions:

A $10-$year bond has a coupon rate of $5\%$ with annual payments and a par value of $$1,000.$ If the appropriate discount rate $($YTM$)$ is $4\mathrm{.}5\%,$ what is the bond's price today?

A $10-$year bond has a coupon rate of $4\%$ with semiannual payments and a par value of $$1,000.$ If the appropriate discount rate $($YTM$)$ is $3\%,$ what is the bond's price today?

A $10-$ year bond has a coupon rate of $6\%$ with semiannual payments and a par value of $$1,000.$ If the bond matures in ten years and its current price is $$995,$ what is the yield to maturity of this bond?