Question

19. Which of these has the highest effective annual rate (EAR)? (In case you forgot, e = 2.71828) A. 10.2% quoted rate, annual compounding B. 10.0% quoted rate, monthly compounding C. 9.8% quoted rate, daily compounding D. 10.1% quoted rate, quarterly compounding

Answer 1

EAR = (1 + r/m)^m - 1

Where, r = quoted rte

             m =number of compounding period in a year

A) EAR = (1 + 0.102 / 1)¹ - 1 = 0.102   or 10.2%

B) EAR = (1 + 0.10 / 12)¹² - 1 = 1.1047 - 1 = 0.1047 or 10.47%

C) EAR = (1 + 0.098 / 365)³⁶⁵ - 1 = 1.1029 - 1 = 0.1029 or 10.29%

D) EAR = (1 + 0.101 / 4)⁴ - 1 = 1.1049 - 1 = 0.1049 or 10.49%

Thus, option [D] has the highest effective annual rate.