Question

Big Dom’s Pawn Shop charges an interest rate of 27 percent per month on loans to its customers. Like all lenders, Big Dom must report an APR to consumers. a. What rate should the shop report? b. What is the effective annual rate? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Annual Percentage Rate (APR)

The APR is calculated by multiplying the interest rate per period with the number of periods compounded per year

Interest Rate per month = 27% per month

Number compounding periods = 12 Months

Therefore, the APR = Interest Rate per month x Number compounding periods

= 27% x 12 Months

= 324%

“Hence, the APR to consumers would be 324%”

Effective Annual Rate (EAR)

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

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

Where, APR = 324%

Number of compounding (n) = 12 Months

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

= [1 + (3.24/12)]¹² – 1

= [1.27] ¹² – 1

= 17.605349 – 1

= 16.605349

= 1,660.53% (Rounded to 2 decimal places)

“Hence, the Effective Annual Rat Interest Rate (EAR) = 1,660.53%”