Determine the equivalent nominal rate of interest compounded semi-annually, as 4.2% compounded monthly.
A) 4.20%
B) 4.24%
C) 4.28%
D) 4.36%
E) 4.44%

Question

Quizplus · Accepted Answer

The equivalent nominal rate of interest compounded semi-annually can be found by first converting the monthly compounded rate to an effective annual rate (EAR) and then converting that EAR to a semi-annual nominal rate. The formula for converting a monthly compounded rate to an EAR is $EAR = (1 + \frac{r}{m})^m - 1$, where $r$ is the annual nominal rate (4.2% or 0.042) and $m$ is the number of compounding periods per year (12 for monthly). Thus, $EAR = (1 + \frac{0.042}{12})^{12} - 1$. After calculating the EAR, convert it to a semi-annual nominal rate by using the formula for nominal interest rate, which is $nominal\ rate = EAR \times m$, where $m$ is now 2 for semi-annual. The calculation will show that the equivalent nominal rate compounded semi-annually is approximately 4.24%.

Determine the Equivalent Nominal Rate of Interest Compounded Semi-Annually, as 4.2