Calculate the duration $($and price$)$ of a bond with the following characteristics: A semi$-$annual payment bond with a $$1,000$ face value, a $4\mathrm{.}5\%$ coupon rate, a $7\mathrm{.}8\%$ YTM$,$ and $8$ years to maturity. Show your table of calculations or show Excel inputs if using the Excel commands.