A company has a $$10,000$ line of credit with a bank. The line of credit calls for an interest rate of $10$ percent and a compensating balance of $5$ percent. This firm needs $$5,000$ of fund to pay for the inventory.

a$)$ How much does the firm need to borrow from the bank?

b$)$ What is the effective interest rate if the firm uses this line of credit with the compensating balance?