If the interest rate (SAIR) is 10% per annum a) What is the effective annual interest rate (EAIR) if the compounding frequency is semi-annual?  b) What about if the compounding frequency is quarterly?  c) What about if the compounding frequency is monthly?  d) What about if the compounding frequency is continuous?   

a) Computation of the effective annual interest rate:-

Effective annual interest rate = (1+Rate/n)^n-1

Here,

n = 2 periods (semiannual)

Effective annual interest rate = (1+10%/2)^2-1

= 1.1025 - 1

= 10.25%

b) Computation of the effective annual interest rate:-

Effective annual interest rate = (1+Rate/n)^n-1

Here,

n = 4 periods (quarterly)

Effective annual interest rate = (1+10%/4)^4-1

= 1.1038 - 1

= 10.38%

c) Computation of the effective annual interest rate:-

Effective annual interest rate = (1+Rate/n)^n-1

Here,

n = 12 periods (monthly)

Effective annual interest rate = (1+10%/12)^12-1

= 1.1047 - 1

= 10.47%

d) Computation of the effective annual interest rate:-

Effective annual interest rate = (e^rate) - 1

= (2.7183^10%) -1

= 1.1052 - 1

= 10.52%