Calculate the equivalent periodic interest rate per payment interval for the following annuity: Semi-annual payments earning 11% compounded quarterly.
A) 5.48991%
B) 5.57563%
C) 5.56812%
D) 5.35654%
E) 5.42639%

Question

Quizplus · Accepted Answer

To find the equivalent periodic interest rate per payment interval for an annuity with semi-annual payments when the nominal annual interest rate is 11% compounded quarterly, we use the formula for converting interest rates: $i_{\text{effective}} = (1 + \frac{r}{m})^m - 1$, where $r$ is the nominal annual rate and $m$ is the number of compounding periods per year. However, since we're looking for a semi-annual equivalent of a quarterly compounded rate, we adjust the formula to find the semi-annual rate: $i_{\text{semi-annual}} = (1 + \frac{0.11}{4})^2 - 1$. This calculation gives us the effective semi-annual interest rate, which matches choice B, 5.57563%.

Calculate the Equivalent Periodic Interest Rate Per Payment Interval for the Following