I'm so stuck.

The Orange County Teachers' Credit Corp. offers an account which pays 14% compounded quarterly. What is its effective rate of yield? (Express your answer to the nearest one-hundredth of a percent.)

To determine the effective rate of yield of an account, compounded quarterly, you first need to understand compound interest. Compound interest refers to the interest on a loan or deposit that is calculated based on the initial principal amount and any accumulated interest from previous periods.

In this case, the interest is compounded quarterly, which means it is calculated and added to the account balance every three months. To calculate the effective rate of yield, we can use the formula:

\(A = P(1 + \frac{r}{n})^{nt}\)

Where:
- A is the final amount (including interest)
- P is the principal (initial deposit or loan amount)
- r is the interest rate (as a decimal)
- n is the number of times interest is compounded per year
- t is the number of years

In our case, the interest rate is 14% or 0.14 as a decimal. Since interest is compounded quarterly, n would be 4 (four times per year). We are not given the duration, so we will assume it is for one year.

Plugging in the values into the formula:

\(A = P(1 + \frac{r}{n})^{nt}\)
\(A = P(1 + \frac{0.14}{4})^{4 \times 1}\)
\(A = P(1 + 0.035)^4\)

To find the effective rate of yield, we need to solve for \((1 + 0.035)^4\) and subtract 1 from the result. This can be done using a calculator or the formula for exponentiation.

\((1 + 0.035)^4 \approx 1.150735\)

Next, subtract 1:

\(1.150735 - 1 \approx 0.150735\)

Finally, convert the decimal to a percentage:

0.150735 * 100 ≈ 15.07%

Therefore, the effective rate of yield for the Orange County Teachers' Credit Corp. account is approximately 15.07%.