What is the semi-annually compounded nominal rate that is equivalent to 10.5% compounded monthly?

A) 11.02%
B) 8.75%
C) 5.37%
D) 10.73%
E) 11.44%

To find the semi-annually compounded nominal rate equivalent to a 10.5% rate compounded monthly, we use the formula for converting interest rates: $(1+\frac{r_m}{m}{)}^m=(1+\frac{r_s}{s}{)}^s$ , where $r_m$ is the monthly rate, $m$ is the number of compounding periods per year for the monthly rate, $r_s$ is the semi-annual rate, and $s$ is the number of compounding periods per year for the semi-annual rate. Given $r_m=10.5\%=0.105$ and $m=12$ , $s=2$ , we solve for $r_s$ . Converting 10.5% monthly to an equivalent semi-annual rate gives approximately 10.73%.