In Exercises $$ 23-28 $$, an account has a rate of $$ 3.5 \% $$. Find the ective annual yield, rounded to the nearest hundredth of a reent, if the interest is compounded 22. semiarnually. 24. quarterly. 25. monthly.

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We use the formula for the effective annual yield (EAY):

$$
\text{EAY} = \left(1+\frac{r}{n}\right)^n - 1,
$$

where:
- $$ r $$ is the nominal annual interest rate (in decimal form), and
- $$ n $$ is the number of compounding periods per year.

Given $$ r = 0.035 $$ (since $$ 3.5\% = 0.035 $$):

---

**1. Compounded Semiannually ( $$ n=2 $$ ):**

$$
\text{EAY} = \left(1 + \frac{0.035}{2}\right)^2 - 1 = \left(1 + 0.0175\right)^2 - 1.
$$

Calculating the square:

$$
\left(1.0175\right)^2 \approx 1.03530625,
$$

so

$$
\text{EAY} \approx 1.03530625 - 1 = 0.03530625.
$$

Rounded to the nearest hundredth of a percent, the effective annual yield is approximately:

$$
3.53\%.
$$

---

**2. Compounded Quarterly ( $$ n=4 $$ ):**

$$
\text{EAY} = \left(1 + \frac{0.035}{4}\right)^4 - 1 = \left(1 + 0.00875\right)^4 - 1.
$$

Calculating $$ (1.00875)^4 $$:

Using a calculator (or logarithms), we find:

$$
(1.00875)^4 \approx 1.03546106,
$$

so

$$
\text{EAY} \approx 1.03546106 - 1 = 0.03546106.
$$

Rounded to the nearest hundredth of a percent, the effective annual yield is approximately:

$$
3.55\%.
$$

---

**3. Compounded Monthly ( $$ n=12 $$ ):**

$$
\text{EAY} = \left(1 + \frac{0.035}{12}\right)^{12} - 1.
$$

Since

$$
\frac{0.035}{12} \approx 0.00291667,
$$

we have

$$
\text{EAY} = \left(1.00291667\right)^{12} - 1.
$$

Using a calculator to compute the exponentiation:

$$
(1.00291667)^{12} \approx 1.03554,
$$

therefore

$$
\text{EAY} \approx 1.03554 - 1 = 0.03554.
$$

Rounded to the nearest hundredth of a percent, the effective annual yield is approximately:

$$
3.55\%.
$$

---

**Summary of Answers:**

- Semiannually: $$ \approx 3.53\% $$
- Quarterly: $$ \approx 3.55\% $$
- Monthly: $$ \approx 3.55\% $$
The effective annual yields are approximately: - Semiannually: 3.53% - Quarterly: 3.55% - Monthly: 3.55%

In Exercises \( 23-28 \), an account has a rate of \( 3.5 \% \). Find the ective annual yield, rounded to the nearest hundredth of a reent, if the interest is compounded 22. semiarnually. 24. quarterly. 25. monthly.

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