You place an order for $1,600$ units of Good X at a unit price of $$53.$ The supplier offers terms of $2/30,$ net $50.$

a$-1.$ How long do you have to pay before the account is overdue?

a$-2.$ If you take the full period, how much should you remit? $($Do not round intermediate calculations and round your answer to the nearest whole number, e$.$g$.,32.)$

b$-1.$ What is the discount being offered? $($Enter your answer as a percent.$)$

b$-2.$ How quickly must you pay to get the discount?

b$-3.$ If you do take the discount, how much should you remit? $($Do not round intermediate calculations and round your answer to the nearest whole number, e$.$g$.,32.)$

c$-1.$ If you don$$t take the discount, how much interest are you paying implicitly? $($Do not round intermediate calculations and round your answer to the nearest whole number, e$.$g$.,32.)$

c$-2.$ How many days$$ credit are you receiving? $($Do not round intermediate calculations and round your answer to the nearest whole number, e$.$g$.,32.)$