First National Bank charges 14.4 percent compounded monthly on its business loans. First United Bank charges 14.7 percent compounded semiannually. Calculate the EAR for First National Bank and First United Bank. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e. g., 32.16.)

The answers are given below

Explanation:

From the question, we are informed that First National Bank charges 14.4 percent compounded monthly on its business loans and that First United Bank charges 14.7 percent compounded semiannually. Calculate the EAR for First National Bank and First United Bank.

The formula to calculate the effective annual rate will be:

EAR = (1+ i/n)^n – 1.

where,

n = number of compounding periods for the year.

First National Bank is compounded monthly on its business loans. This means that n = 12 since there are 12 months in a year.

First United Bank is compounded semiannually. This means that n = 2 since it's compounded semiannually.

EAR for First National Bank will be:

n = 12

I = 14.4% = 14.4/100 = 0.144

EAR = (1+ i/n)^n – 1

= (1 + 0.144/12)^12 - 1

= (1 + 0.012)^12 - 1

= (1.012)^12 - 1

= 0.1539

=15.39%

EAR for First United Bank will be:

n = 2

i = 14.7% = 14.7/100 = 0.147

EAR = (1+ i/n)^n - 1

= (1 + 0.147/2)² - 1

= (1 + 0.0735)² - 1

= (1.0735)² - 1

= 0.1524

= 15.24%

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