Intergrative$-$Comparison of loan terms Cumberland Furniture wishes to establish a prearranged borrowing agreement with a local commercial bank. The bank's terms for a line of credit are $2\mathrm{.}30\%$ over the prime rate, and each year the borrowing must be reduced to zero for a $30-$day period. For an equivalent revolving credit agreement, the rate is $1\mathrm{.}70\%$ over prime with a commitment fee of $0\mathrm{.}5\%$ on the average unused balance. With both loans, the required compensating balance is equal to $10\%$ of the amount borrowed. $($Note: Cumberland currently maintains $$0$ on deposit at the bank.$)$ The prime rate is currently $7\%.$ Both agreements have $$12,000,000$ borrowing limits$.$ The firm expects on average to borrow $$8,000,000$ during the year no matter which loan agreement it decides to use.

a$.$ What is the effective annual rate under the line of credit?

b$.$ What is the effective annual rate under the revolving credit agreement? $($Hint: Compute the ratio of the dollars that the firm will pay in interest and commitment fees to the dollars that the firm will effectively be able to use.$)$

c$.$ If the firm does expect to borrow an average of half the amount available, which arrangement would you recommend for the borrower? Explain why.