A stock had returns of $24\%,-13\%,$ and $44\%$ in each of the past three years. Over the past four years, the arithmetic average annual return for the stock was $17\mathrm{.}75\%.$ What was the geometric return for the stock over the past four years? Note that individual stock returns are only given for each of the past three years, but that the question asks about the geometric return over the past four years.

$15\mathrm{.}86\%($plus or minus $0\mathrm{.}02$ percentage points$)$

$15\mathrm{.}82\%($plus or minus $0\mathrm{.}02$ percentage points$)$

$32\mathrm{.}77\%($plus or minus $0\mathrm{.}02$ percentage points$)$

$16\mathrm{.}00\%($plus or minus $0\mathrm{.}02$ percentage points$)$

None of the above is within $0\mathrm{.}02$ percentage points of the answer