A bond with a face $($par$)$ value of $$1,000$ that matures in one year has a coupon rate of $4\%,$ paid annually. If market interest rates $($for example, rafes on new bonds$)$ are $2\mathrm{.}5\%,$ what bond? What is the bond's Yield to Maturity $($YTM$)?$

$$1014\mathrm{.}63$

$($b$)$ Suppose the price moves to $$980.$ What is the bond's yield to maturity?

$($c$)$ Suppose the price of this bond increases to $$1000.$ What is the bond's Yield to Maturity?