Your firm's bank has offered you two options for short-term financing in the amount of $500,000. The first option is a committed line of credit with a commitment fee of 0.4% (EAR) and an interest rate of 8% (APR, compounded quarterly). The second option is a loan with a 3% compensating balance and an interest rate of 7.6% (APR, compounded quarterly). If you need $485,000 in financing at the beginning of the year and plan to pay it back at the end of the year, which option has a lower effective annual rate of interest?
The EAR of the 8% APR compounded quarterly is ___%(Round to three decimal places.)
The EAR of the 7.6% APR compounded quarterly is __%(Round to three decimal places.)
The effective annual rate of interest for the first option is __%(Round to three decimal places.)
The effective annual rate of interest for the second option is __%(Round to three decimal places.)
| 1] | EAR = 1.02^4-1 = | 8.243% |
| 2] | EAR = 1.019^4-1 = | 7.819% |
| 3] | Interest charges = 485000*8.243% = | $ 39,978.55 |
| Commitment charges = 15000*0.4% = | $ 60.00 | |
| Total financing charges | $ 40,038.55 | |
| EAR = 40038.55/485000 = | 8.255% | |
| 4] | Loan required [including amount for compensating balance} = 485000/(100%-3%) = | $ 5,00,000 |
| Interest charges = 500000*7.819% = | $ 39,095.00 | |
| EAR = 39095/485000 = | 8.061% |
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