$($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$)$

$($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.