First National Bank charges 14.1 percent compounded monthly on its business loans. First United Bank charges 14.4 percent compounded semiannually.
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Calculate the EAR for First National Bank and First United Bank. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
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EAR | |
First National | % |
First United | % |
As a potential borrower, which bank would you go to for a new loan? |
First United Bank |
For discrete compounding, to find the EAR, we use the equation: |
EAR = [1 + (APR / m)]m − 1 |
So, for each bank, the EAR is: |
First National: EAR = [1 + (.141 / 12)]12 − 1 = .1505, or 15.05% |
First United: EAR = [1 + (.144 / 2)]2 − 1 = .1492, or 14.92% |
Notice that the higher APR does not necessarily mean the higher EAR. The number of compounding periods within a year will also affect the EAR.
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Calculator Solution: |
Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.
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Enter
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14.1%
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12
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NOM
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EFF
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C/Y
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Solve for
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15.05%
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Enter
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14.4%
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2
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NOM
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EFF
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C/Y
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Solve for
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14.92%
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