Consider a coupon bond with a yield to maturity of $10\%$ and time to maturity of $5$ years. It is currently priced at par $($price $=$ par value$).$ Eplain why each of the following statements is true or false.

A$.$ The bond's yield to maturity would remain unchanged until to maturity.

B$.$ If we purchase the bond now, hold it until to maturity, and reinvest the coupons received at $11\%$ reinvestment rate, then we will earn $10\%$ rate of return over the entire holding period.

C$.$ The current bond price implies that the market interest rate is equal to $10\%.$

D$.$ If you require $8\%$ rate of return, you will not purchase the bond because you think the bond is currently overvalued