Contemporary Furnishings received an invoice on April $18$ from Palliser Furniture. The invoice for $$18,976\mathrm{.}45$ was dated April $16$ with terms $\frac{2}{15},\frac{1}{30},\frac{n}{45}.$

a$.$ What is the balance after a payment of $$10,000$ on May $1?($Round intermediate calculations and final answer to $2$ decimal places.$)$

Balance owed

$

b$.$ What additional payment on May $15$ will settle the account? $($Round intermediate calculations and final answer to $2$ decimal places.$)$

Additional payment

$