A life insurance company will sell a $20-$year annuity paying $$1600$ at the end of each month for $$175,000.$ What quarterly compounded nominal rate of interest will the annuitant earn?

Multiple Choice

$9\mathrm{.}226\%$

$9\mathrm{.}401\%$

$9\mathrm{.}297\%$

$8\mathrm{.}735\%$

$9\mathrm{.}335\%$