Which is most true of an annual rate of 4% compounded quarterly?
A) It is equivalent to 4.4% paid annually.
B) It is equivalent to 16.99% paid annually.
C) It is equivalent to 1% simple interest paid quarterly.
D) It is equivalent to 4.06% paid annually.

Question

Quizplus · Accepted Answer

When interest is compounded quarterly, the effective annual rate (EAR) is calculated using the formula $(1 + \frac{r}{n})^n - 1$, where $r$ is the annual nominal rate (0.04 in this case) and $n$ is the number of compounding periods per year (4 for quarterly). Plugging in the values, we get $(1 + \frac{0.04}{4})^4 - 1 = (1.01)^4 - 1 \approx 0.0406$ or 4.06%, making option D correct.

Which Is Most True of an Annual Rate of 4