$1.$ A $15-$year bond with $5\%$ coupons, payable semi$-$annually, is priced with a s$.$a$.$ yield of $5\mathrm{.}4\%.$

a$.$ What is the $($modified$)$ duration of this bond? Use the spreadsheet to compare exact value with approximation when $$i$=\mathrm{.}005.$

b$.$ Compare the exact price of this bond with a yield of $5\mathrm{.}0\%,$ to the price approximated with the current price $($from PS $2)$ and exact duration. $$