If a bond's yield to maturity does not change, the return on the bond each year will be

equal to the yield to maturity. Confirm this for both a premium and a discount bond

using a $4-$year $3$ percent coupon bond with annual coupon payments and a face value of

$$1,000.$

Bond a$.$Assume the yield to maturity is $2$ percent, what is the bond price today, what is the bond price in one year, and what is the rate of return?

Bond b$.$Assume the yield to maturity is $4$ percent,$$ what is the bond price today, what is the bond price in one year, and what is the rate of return?