First National Bank charges 13.7 percent compounded monthly on its business loans. First United Bank charges 14 percent compounded semiannually.

Problem 6-14 Calculating EAR [LO4]

First National Bank charges 13.7 percent compounded monthly on its business loans. First United Bank charges 14 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 United Bank

 

Explanation:

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 + (.137 / 12)]12 − 1 = .1459, or 14.59%

First United: EAR = [1 + (.140 / 2)]2 − 1 = .1449, or 14.49%

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.

   

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

  

Enter	13.7%						12
		NOM			EFF			C/Y
Solve for				14.59%

  

Enter	14.0%						2
		NOM			EFF			C/Y
Solve for				14.49%