I have been trying to solve the following problem all week. I cannot figure out to set any of it up. My teacher absolutely refuses to help at all. My classmates will not respond to any emails. Can someone please help? I would greatly appreciate it!

Bank A offers the following terms for a $10 million loan:
- interest rate: 8% for one year on funds borrowed
- fees: 0.5% of the unused balance for the unused term of the loan

Bank B offers the following terms for a $10 million loan:
- interest rate: 6.6% for one year on funds borrowed
- fees: 2% origination fee

a. Which terms are better if the firm intends to borrow the $10 million for the entire year?

b. If the firm plans to use the funds for only three months, which terms are better?

The book provides the answers, but I have no idea how to even set these up. Part a.) bank A is 8%, bank B is 6.73%. Part b.) bank A is 9.5%, bank B is 6.73%.
Pleasehelpme
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Joined: Sun Jun 20, 2010 8:36 pm

For Bank A, the fee is only incurred if the funds are borrowed for less than the full year. So under the full-year scenario, the cost of borrowing from A is only the stated rate.

If the loan is repaid to A after just one quarter, though, the borrower will pay an annual rate of 8% on the 10M (for one quarter), and then 1/2 of 1% on the 10M for the remaining 9 months.

Using that info, calculate the total interest that'll be paid to A under a 3-month borrowing. Then multiply it by 4 to get the 'annuallized' effective interest, since this interest is paid for a loan that's only outstanding for 3 months. Compare that amount to 10M and see what effective rate you get.

Bank B has a different fee structure. They charge 6.6% on the 10M, but with a 2% origination fee, the borrower is only receiving 98% of the total loan amount; i.e. 9,800,000. Thus the borrower is paying total interest of 6.6% x 10M, against a loan amount of 9.8M. What effective rate does that represent?

Since B's fee structure isn't affected by the length of time the loan is outstanding (as A's is), the effective cost of borrowing from B is the same whether it's for a full year, or just 3 months.