A firm plans to invest $$400,000$ in a new high$-$efficiency furnace that will reduce its energy bill by $$100,000$ in years $1$ and $2,$ $$75,000$ in years $3,4,$ and $5,$ and $$50,000$ in years $6$ through $10.$ Calculate the project's internal rate of return. $($Use your financial calculator.$)$

Multiple choice question.

$13\mathrm{.}07\%$

$12\mathrm{.}7\%$

$10\mathrm{.}08\%$

$11\mathrm{.}19\%$