The Black Horse is currently considering a project that will produce cash inflows of $$12,000$ a year for three years followed by $$6,500$ in year $4.$ The cost of the project is $$38,000.$ What is the profitability index if the discount rate is $7$ percent?

Group of answer choices

$1\mathrm{.}04$

$1\mathrm{.}09$

$0\mathrm{.}96$

$0\mathrm{.}99$

$1\mathrm{.}12$