A financial instrument provides three future cash flows:

$$1,406\mathrm{.}01$ at the end of $2$ years

$$2,596\mathrm{.}43$ at the end of $8$ years

$$1,172\mathrm{.}62$ at the end of $13$ years

Calculate the duration $($D$)$ of the financial instrument at a yield of $7\%$ pa compounded yearly. Give your answer in years to $2$ decimal places

$.$

$D=$ years