A four$-$year option$-$free bond has a par value of R$1000,$ has an annual coupon rate of $9$ percent and trades at a yield to maturity of $7$ percent. The current bond price is R$1067\mathrm{.}74.$ The yield to maturity is expected to increase by $100$b$.$p$.$

Calculate the duration of the bond. $(12$ marks$)$

Assuming that the bond$$s convexity is $195,$ use duration$-$with$-$convexity to calculate the price of the bond at the new yield. $(4$ marks$)$

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