Cost of Borrowing [LO3] You\'ve worked out a line of credit arrangements that al
ID: 2806154 • Letter: C
Question
Cost of Borrowing [LO3] You've worked out a line of credit arrangements that allow you to borrow up to $50 million at any time. The interest rate is 53 percent per month. Also, 5 percent of the amount that you borrow must be deposited in a non-interests-bearing account.Assume that your bank uses compound interest on its line of credit loans. a. What is the effective annual interest rate on this lending arrangement? b. Suppose you need $15 million today and you repay it in six months. How much interest will you pay?
Explanation / Answer
Monthly interest rate (i) = 0.53%
Amount of monthly interest (INT)= $50,000,000 x 0.53%
= $265,000
Amount of money received after 5% compensating balance (PV) = $50,000,000x (1-0.05)
= $47,500,000
Effective annual rate = (1+ INT/PV)^12 -1
= ( 1+ 265,000 / 47,500,000)^12 -1
= 1.0690-1
= 6.90%
Part B
Interest for 6 months
Interest = Prin x Rate x period
= 15,000,000 x 0.53% x 6
= $477,000