First National Bank charges 13.4 percent compounded monthly on its business loans. First United Bank charges 13.7 percent compounded semiannually.
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.)
EAR
First National %
First United %
As a potential borrower, which bank would you go to for a new loan?
First National Bank
First United Bank

Effective Annual Rate (EAR) is the equivalent annual interest rate where the interest rate for a transaction is quoted to be compounded for a period shorter that a year.

Usually , where the interest nominal interest rate is quoted to be compounded for a shorter period than a year, the EAR is usually higher. The EAR is computed as follows using this formula:

EAR =( (1+r/m)^(m) - 1 ) × 100

r- nominal interest rate per annum, m- number of compounding periods in a year

So we can compute the EAR for the two banks :

First National Bank:

m= 12 compounding periods in a year

Monthly interest rate = r/m = 13.4%/12 = 0.01116

EAR = (1 + 0.01116)^(12) - 1

= 14.25%

First United Bank:

m = 2 compounding periods in a year

Semi-annual interest rate = 13.7%/2 = 0.0685

EAR = (1+0.0685)^(2) -1

= 14.17%

As a potential borrower, I would go for First United Bank, as it offers a lower rate, which implies a lower interest cost on the loan.

First National Bank-14.25%

First United Bank-14.17%