Question

The 3-month risk-free interest rate is 2% effectively. What is the effective annual interest rate (EAR)? Leave your answer in decimals with 3 significant figures. (E.g. 6.12% as 0.0612)

Answer 1

Effective Interest rate for 3 months = 2%

Let us assume that there is quarterly compounding. There are 4 quarters in an year. So, No. of Compounding periods = 4

Effective Annual interest Rate (Quarterly compounding) = [1 + interest rate for a quarter]^{No.of compounding Periods} - 1 = (1+0.02)⁴ - 1 = 8.24% =  0.0824

Let us assume that there is monthly compounding. There are 12 months in an year. So, No. of Compounding periods = 12

Effective Annual interest Rate (monthly compounding) = [1 + nominal interest rate for a month]^{No.of compounding Periods} - 1 = [1+(0.02/3)]¹² - 1 = 8.29% =  0.0829