If the one year rate expressed with semi-annual compounding is 6%,what is the equivalent rate with quarterly compounding.
A)3.00%
B)5.87%
C)5.96%
D)6.00%

Question

Quizplus · Accepted Answer

To find the equivalent rate with quarterly compounding when given a semi-annual compounding rate, we use the formula to convert interest rates: $ (1 + \frac{r_{m}}{m})^{m} = (1 + \frac{r_{n}}{n})^{n} $, where $r_{m}$ is the rate with compounding frequency $m$ and $r_{n}$ is the rate with compounding frequency $n$. For semi-annual compounding at 6%, $r_{m} = 0.06$ and $m = 2$. We want to find $r_{n}$ with $n = 4$ (quarterly compounding). Rearranging the formula and solving for $r_{n}$, we find that the equivalent quarterly rate is approximately 5.96%.

If the One Year Rate Expressed with Semi-Annual Compounding Is