Shiing Shen Chern's credit card company determines his minimum monthly payment by adding all new interest to $1\%$ of the outstanding principal. The credit card company charges an interestrate of $0\mathrm{.}039776\%$ per day. On March $16,$ Shiing uses his credit card to purchase airline tickets for his family for $$3000.$ He makes no other purchases during March. Use the given information and the rule that minimum payments are rounded up to the nearest dollar to answer parts a and $b$ below.

a$)$ Assuming Shiing had no new interest, determine Shiing's minimum payment due on April $1,$ his billing date.

Shiing's minimum payment due on April $1$ is $$30.$

b$)$ On April $1,$ instead of making the minimum payment, Shiing makes a payment of $$700.$ Assuming there are no additional charges or cash advances, determine Shiing's minimum payment due on May $1.$

Shiing's minimum payment due on May $1$ is $$.$