Bond prices and yields $($S$3\mathrm{.}1)$ Construct some simple examples to illustrate your answers to the following:

a$.$ If interest rates rise, do bond prices rise or fall?

b$.$ If the bond yield to maturity is greater than the coupon, is the price of the bond greater or less than $100?$

c$.$ If the price of a bond exceeds $100,$ is the yield to maturity greater or less than the coupon?

d$.$ Do high$-$coupon bonds sell at higher or lower prices than low$-$coupon bonds?

e$.$ If interest rates change, do the prices of high$-$coupon bonds change proportionately more than that of low$-$coupon bonds?