Magenta Company received an invoice of $$27,700$ for catering services at their annual company picnic. The invoice was dated May $6,2013$ and had the following payment terms $\frac{7}{10},\frac{3}{15},\frac{n}{30}.$

a$.$ Calculate the amount required to settle the invoice on May $14,2013$

Round to the nearest cent

b$.$ Calculate the amount required to settle the invoice on May $19,2013$

c$.$ How much money would the company save by settling the invoice within the first discount period rather than settling it within the second discount period?

Round to the nearest cent