A financial instrument provides three future cash flows:

$$1,318\mathrm{.}27$ at the end of $5$ years

$$2,142\mathrm{.}06$ at the end of $7$ years

$$2,288\mathrm{.}93$ at the end of $13$ years

Calculate the duration $($D$)$ of the financial instrument at a yield of $9\%$ pa compounded yearly. Give your answer in years to $2$ decimal places.

D $=$ years