Question

What is the EAR corresponding to a nominal rate of 8% compounded semiannually? Compounded quarterly? Compounded daily?

Answer 1

Semi-annual compounding:

Compute the effective annual rate (EAR), using the equation as shown below:

EAR = {1 + (Rate/ Compounding periods)}^{Compounding periods} – 1

         = {1 + (0.08/ 2)}² – 1

         = (1 + 0.04)² – 1

         = 8.16%

Hence, the EAR is 8.16%.

Quarterly compounding:

Compute the effective annual rate (EAR), using the equation as shown below:

EAR = {1 + (Rate/ Compounding periods)}^{Compounding periods} – 1

         = {1 + (0.08/ 4)}⁴ – 1

         = (1 + 0.02)⁴ – 1

         = 8.243216%

Hence, the EAR is 8.243216%.

Daily compounding:

Compute the effective annual rate (EAR), using the equation as shown below:

EAR = {1 + (Rate/ Compounding periods)}^{Compounding periods} – 1

         = {1 + (0.08/ 365)}³⁶⁵ – 1

         = (1 + 0.00021917808)³⁶⁵ – 1

         = 8.327757092%

Hence, the EAR is 8.327757092%.