Question

What is the effective annual rate​ (EAR) of a car loan that is advertised at 5​% (APR) and paid with weekly

​paymenst? round to two decimal place.

Please give an explanation to what you are doing as you answer. Thanks.

Answer 1

Effective Annual Rate (EAR)

Effective Interest Rate (EAR) is calculated by using the following formula

Effective Interest Rate = [1 + (r/ n)] n − 1

Where, Annual Interest Rate (r) = 5.00% per year

Number of compounding period (n) = 52 Weeks

Therefore, the Effective Interest Rate (EAR) = [1 + (r/ n)] n − 1

= [1 + (0.05/52)]52 – 1

= [1 + 0.000961538462]52 – 1

= 1.051245842 – 1

= 0.051245842 or

= 5.12% (Rounded to 2 decimal place)

“Hence, the Effective Annual Rate (EAR) will be 5.12%”