What is the monthly compounded nominal rate that is equivalent to 7.8% compounded semi-annually?
A) 6.40%
B) 7.68%
C) 8.12%
D) 3.90%
E) 5.88%

Question

Quizplus · Accepted Answer

To find the equivalent monthly compounded nominal rate from a semi-annual rate, we use the formula for converting interest rates: $ (1 + \frac{r_{SA}}{2})^2 = (1 + \frac{r_M}{12})^{12} $, where $r_{SA}$ is the semi-annual rate and $r_M$ is the monthly rate. Given a 7.8% semi-annual rate, or 0.078, we solve for $r_M$. Rearranging and solving gives an equivalent monthly rate of approximately 7.68%.

What Is the Monthly Compounded Nominal Rate That Is Equivalent