To determine whether the effective annual rate (EAR) of 5% compounded monthly is approximately 5%, we need to calculate the EAR using the formula:
EAR = (1 + r/n)^(nt) – 1
Where:
- r = nominal interest rate (5% or 0.05)
- n = number of compounding periods per year (12 for monthly)
- t = number of years (1, in this case)
Plugging in the values, we get:
EAR = (1 + 0.05/12)^(12*1) – 1
Calculating that:
EAR = (1 + 0.00416667)^(12) – 1
EAR = (1.00416667)^(12) – 1
EAR ≈ 0.051161 or 5.1161%
This means that the effective annual rate is approximately 5.1161%, which is greater than 5%. Thus, the statement is false.