A bond has just been issued. The bond has an annual coupen rate of $8\%$ and coupons are paid annually. The bond has a face value of $$1,000$ and will mature in $8$ years. The bond's yield to maturity is $9\%.$

a$.$ Calculate the actual currency change in the bond's price as the yield to maturity changes from $9\%$ to $9\mathrm{.}75\%.$

b$.$ Use the bond's duration to calculate the bond's approximate currency price change as the yield to maturity changes from $9\%$ to $9\mathrm{.}75\%$