Question

8. A given rate is quoted as 12% APR, but has an effective annual rate (EAR) of 12.55%. What is the frequency of compounding during the year? a. Annually b. Semiannually c. Quarterly d. Monthly e. Daily

Answer 1

Effective annual rate (EAR) if the Compounding is annually

Effective annual rate = 12.00%

Effective annual rate (EAR) if the Compounding is semi-annually

Effective annual rate = [1 + (0.12/2)]^2 - 1

Effective annual rate = [1 + 0.06]^2 - 1

Effective annual rate = 1.1236 - 1

Effective annual rate = 0.1236 or 12.36%

Effective annual rate (EAR) if the Compounding is Quarterly

Effective annual rate = [1 + (0.12/4)]^4 - 1

Effective annual rate = [1 + 0.03]^4 - 1

Effective annual rate = 1.12550881 - 1

Effective annual rate = 0.12550881 or 12.55%

Therefore, the frequency of compounding during the year is (c)-Quarterly