Assume you have a $1-$year investment horizon and are trying to choose among three bonds. All have

the same degree of default risk and mature in $10$ years. The first is a zero$-$coupon bond that pays

$$1,000$ at maturity. The second has an $8\%$ coupon rate and pays the $$80$ coupon once per year. The

third has a $10\%$ coupon rate and pays the $$100$ coupon once per year.

a$)$ If all three bonds are now priced to yield $8\%$ to maturity, what are the prices of: $($i$)$ the zero$-$

coupon bond; $($ii$)$ the $8\%$ coupon bond; $($iii$)$ the $10\%$ coupon bond?

b$)$ If you expect their yields to maturity to be $8\%$ at the beginning of next year, what will be the

price of each bond?