$($i$)$ A Treasury bond with $100$ maturity face value has a $9$ annual coupon and $15$ years left to maturity. What price will the bond sell for assuming that the $15$ year yield to maturity in the market is $4\%,9\%$ and $14\%$ respectively? $($Show your workings in full$)(8$ marks$)$

$($ii$)$ Without using any further calculations, comment on whether the price movements would have been greater or smaller if instead of using a $15$ year bond a $10$ year bond had been used. $(2)$