Luther Industries is offered a $1 million dollar loan for four months at an APR of 9%.If Luther's bank requires that the firm maintain a compensating balance equal to 10% of the loan amount in a non-interest bearing account,then the effective annual rate EAR for this loan is closest to:

Question

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A)The origination fee is charged on the principal of the loan.The amount of the compensating balance is equal to .10 × $1,000,000 = $100,000,so that the actual proceeds from the loan = $1,000,000 - $100,000 = $900,000.The interest on the loan equals $1,000,000 × 11ea7cce_3c37_fa21_928c_8d5ebd6cbc88_TB1626_11 × 4 months = $30,000 The actual four month interest rate is: 11ea7cce_3c37_fa22_928c_5bfd98827337_TB1626_11 - 1 = .144444 or 14.44% Expressing this rate as an EAR gives 1.14444^(12/4) - 1 = .4989 or 49.89%

Luther Industries Is Offered a $1 Million Dollar Loan for Four