A pension plan is obligated to make disbursements of $$1\mathrm{.}1$ million, $$2\mathrm{.}1$ million, and $$1\mathrm{.}1$ million at the end of each of the next three years, respectively. Find the duration of the plan's obligations if the interest rate is $11\%$ annually. $($Do not round intermediate calculations. Round your answer to $4$ decimal places.$)$