A bank offers your firm a revolving credit arrangement for up to $70 million at

Question

A bank offers your firm a revolving credit arrangement for up to $70 million at an interest rate of 2.3 percent per quarter. The bank also requires you to maintain a compensating balance of 4 percent against the unused portion of the credit line, to be deposited in a non-interest-bearing account. Assume you have a short-term investment account at the bank that pays 1.20 percent per quarter, and assume that the bank uses compound interest on its revolving credit loans.
a. What is your effective annual interest rate (an opportunity cost) on the revolving credit arrangement if your firm does not use it during the year?
The EAR





b. What is your effective annual interest rate on the lending arrangement if you borrow $45 million immediately and repay it in one year?







c. What is your effective annual interest rate if you borrow $70 million immediately and repay it in one year?

Explanation / Answer

GIVEN:
Interest rate = 2.3 %
Credit = 7 million $
Compensating balance = 4%
a.)Solution:
                                                       Interest rate * principal amount
Effective annual interest rate = ----------------------------------------------------
                                                    principal - compensating balance


                                                  0.023 * 7000000
                                            = ------------------------
                                                    7000000 - 0.04
                                              

                                                161000
                                            = ----------
                                               6999999.96
                                           

                                             = 0.023 %

b.) GIVEN :
Principal amount = 45000000
Interest rate = 2.3%



Interest rate for one year =       interest rate * principal amount
                                              ----------------------------------------
                                                  Proceeds * principal amount
                                         

                                       =               0.023 * 45000000
                                                    ----------------------------
                                                       1 * 45000000

                                                          1035000
                                      =                 ------------
                                                         45000000
                                      =                   0.023 %

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