Find the APR, or stated rate, in each of the following cases

Problem 6-13 Calculating APR [LO4]
Find the APR, or stated rate, in each of the following cases (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.):

Here we are given the EAR and need to find the APR. Using the equation for discrete compounding:
EAR = [1 + (APR/m)]m − 1
We can now solve for the APR. Doing so, we get:
APR = m[(1 + EAR)1/m – 1]
EAR = .109 = [1 + (APR/2)]2 − 1	APR = 2[(1.109)1/2 − 1] = .1062, or 10.62%
EAR = .118 = [1 + (APR/12)]12 − 1	APR = 12[(1.118)1/12 − 1] = .1121, or 11.21%
EAR = .095 = [1 + (APR/52)]52 − 1	APR = 52[(1.095)1/52 − 1] = .0908, or 9.08%
Solving the continuous compounding EAR equation:
EAR = eq − 1
We get:
APR = ln(1 + EAR)
APR = ln(1 + .132)
APR = .1240, or 12.40%

   

Calculator Solution:

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

  

Enter				10.9%			2
		NOM			EFF			C/Y
Solve for	10.62%

  

Enter				11.8%			12
		NOM			EFF			C/Y
Solve for	11.21%

  

Enter				9.5%			52
		NOM			EFF			C/Y
Solve for	9.08%

Answer