A new bottling machine will cost $$1,200$ initially. The machine will produce after$-$tax cash flow of $$500$ in year $1,$$$600$ in year $2,$$$700$ in year $3,$ and $$800$ in year $4.$ Your company's cost of capital is $8\mathrm{.}2\%.$ What is the modified internal rate of return $($MIRR$)?$

a$.36\mathrm{.}20\%$

b$.17\mathrm{.}26\%$

c$.24\mathrm{.}61\%$

d$.10\mathrm{.}00\%$