Question

If the nominal interest rate (r) is 20% per year and is monthly compounded (n=12), what is the effective annual rate (a)? A) 21.94% B) 20% C) 19.68% D) 66.67%

Answer 1

The effective annual rate (EAR) when the nominal interest rate is 20% per year and is monthly compounded is 21.94%, which corresponds to option A.

Step-by-step explanation:

If the nominal interest rate (r) is 20% per year and is monthly compounded (n=12), to find the effective annual rate (EAR or a), we use the formula:

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

Where:

r = nominal interest raten = number of compounding periods per year

Substituting the given values:
EAR = (1 + 0.20/12)^(12) - 1

EAR = (1 + 0.01666667)^(12) - 1

EAR = (1.01666667)^(12) - 1

EAR = 1.2194 - 1

EAR = 0.2194, or 21.94%

Therefore, the effective annual rate is 21.94%, corresponding to option A.