First National Bank (bank a) charges an APR of 13.1 percent compounded monthly on its business loans. First United Bank (bank b) charges an APR of 13.3 percent compounded semiannually. As a potential borrower, which bank would you go to for a new loan?

As EAR for First United Bank is less than EAR for First National Bank so I would go to First United Bank for a new business loan.

Explanation:

In order to solve this question, we need to understand what Effective Annual Rate (EAR) and  Annual Percentage Rate (APR) is.

Effective Annual Rate (EAR):

The rate of interest earned by taking compound interest into account in a year is called Effective Annual Rate (EAR).

Annual Percentage Rate (APR):

The rate of interest described as a yearly rate is called  Annual Percentage Rate (APR).

Formula for calculating EAR:

EAR = ( 1 + APR / m )^m-1

where

EAR = Effective Annual Rate

APR = Annual Percentage Rate

m = compounding periods

Calculation for First National Bank:

By putting the values in the above formula, we get

EAR for First national Bank = ( 1 + .131 / 12 )^12 - 1

EAR = 13.92%

Calculation for First United Bank:

By putting the values in the above formula, we get

EAR for First United bank = ( 1 + .134 / 2 )^2 - 1  

EAR = 13.85%

As EAR for First United Bank is less than EAR for First National Bank so I would go to First United Bank for a new business loan.

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