Arnell Industries has $$25$ million in permanent debt outstanding. The firm will pay interest only on this debt.$$ Arnell's marginal tax rate is expected to be $30\%$ for the foreseeable future.

a$.$ Suppose Arnell pays interest of $8\%$ per year on its debt. What is its annual interest tax$$ shield?

b$.$ What is the present value of the interest tax$$ shield, assuming its risk is the same as the$$ loan?

c$.$ Suppose instead the interest rate on the debt were $5\%.$ What is the present value of the interest tax shield in this$$ case?