Consider the following cashflow. Now is time $t=0,$ with time measure in years.

There will be $6$ annual payments of $100$ each, starting with the first payment at

$t=1.$ At $t=10,$ there will be a payment of $200.$

Assuming the current term structure is flat at $i=\mathrm{.}09,$ what is the Macaulay

duration of the cashflow?