On September $26,2010,$ Austin received $$2,750$ from her father. She settled this amount on March $6,2011$ with interest of $$140\mathrm{.}78.$

No written response required.

a$.$ What was the time period of the loan, expressed in days $($rounded up to the next day$)?$

$170$

$161$

$156$

$177$

b$.$ What was the annual rate of simple interest charged for this loan?

$1\mathrm{.}16\%$

$0\mathrm{.}32\%$

$3\mathrm{.}82\%$

$11\mathrm{.}61\%$