a$)$ What is the difference between the coupon and the yield to maturity of a bond?

b$)$ Why would the coupon exceed the yield and vice versa?

c$)$ Why is the yield on a $10$y US T$-$bond higher than on a $10$y German Government Bond $($known as a Bund$)?$

$2.$ A $30-$year Treasury bond is issued with a par value of $$100,$ paying a coupon of $6\%$ or $$60$ per year. If interest rates increase after the T$-$bond is issued, what happens to the bond$$s a$)$ coupon rate? b$)$ price? c$)$ yield to maturity?

$3.$ If a bond with par value of $$1,000$ and a coupon of $8\%$ is selling at a price of $$970,$ is the bond$$s yield to maturity more or less than $8\%?$