To settle a $$580$ invoice, Anna can pay $$570$ now or the full amount $45$ days later.

a$.$ Which alternative should she choose if money can earn $13\frac{3}{4}\%?$

Pay $$570$ now

Pay full amount $45$ days later

b$.$ What rate would money have to earn for Anna to be indifferent between the alternatives? $($Use $365$ days a year. Do not round intermediate calculations and round your final answer to $2$ decimal places.$)$

Rate $\%$