A $5-$year bond with a yield of $5\%($continuously compounded$),$ pays an $6\%$ coupon at the end of each year, with a face value of $$100?$

Check the results from your previous duration calculation the long way.

HINT: Recalculate the bond's price at the new rate or on the basis of a $4\mathrm{.}8\%$ per annum yield $($meaning it was reduced by $.2\%)$ and verify that the result is in agreement with your answer to the previous question. Show your work. Please do this