Find the effective annual yield for a passbook savings account that has a rate of $$ 9 \% $$ compounded monthly, Round the answer to the nearest tenth of a percent. $$ .0 .0938 \% $$ $$ 10.0 \% $$ $$ 9.0 \% $$ $$ 9.4 \% $$

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To find the effective annual yield (EAY) for a savings account with a nominal interest rate compounded monthly, we can use the formula:

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

Where:
- $$ r $$ is the nominal interest rate (as a decimal),
- $$ n $$ is the number of compounding periods per year,
- $$ t $$ is the number of years.

In this case:
- $$ r = 0.09 $$ (since $$ 9\% = 0.09 $$),
- $$ n = 12 $$ (monthly compounding),
- $$ t = 1 $$ (for one year).

Now, we can substitute these values into the formula:

$$
EAY = \left(1 + \frac{0.09}{12}\right)^{12 \cdot 1} - 1
$$

Let's calculate this step by step.

1. Calculate $$ \frac{0.09}{12} $$.
2. Add 1 to the result.
3. Raise the result to the power of 12.
4. Subtract 1 from the final result.
5. Convert to a percentage and round to the nearest tenth of a percent.

Now, I will perform these calculations.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{0.09}{12}$$
- step1: Convert the expressions:
  $$\frac{\frac{9}{100}}{12}$$
- step2: Multiply by the reciprocal:
  $$\frac{9}{100}\times \frac{1}{12}$$
- step3: Reduce the numbers:
  $$\frac{3}{100}\times \frac{1}{4}$$
- step4: Multiply the fractions:
  $$\frac{3}{100\times 4}$$
- step5: Multiply:
  $$\frac{3}{400}$$
Calculate or simplify the expression $$ (1 + 0.09/12)^12 - 1 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(1+\frac{0.09}{12}\right)^{12}-1$$
- step1: Divide the terms:
  $$\left(1+\frac{3}{400}\right)^{12}-1$$
- step2: Add the numbers:
  $$\left(\frac{403}{400}\right)^{12}-1$$
- step3: Rewrite the expression:
  $$\frac{403^{12}}{400^{12}}-1$$
- step4: Reduce fractions to a common denominator:
  $$\frac{403^{12}}{400^{12}}-\frac{400^{12}}{400^{12}}$$
- step5: Transform the expression:
  $$\frac{403^{12}-400^{12}}{400^{12}}$$
Let's go through the calculations step by step:

1. **Calculate $$ \frac{0.09}{12} $$**:
   $$
   \frac{0.09}{12} \approx 0.0075
   $$

2. **Add 1 to the result**:
   $$
   1 + 0.0075 = 1.0075
   $$

3. **Raise the result to the power of 12**:
   $$
   (1.0075)^{12} \approx 1.093807
   $$

4. **Subtract 1 from the final result**:
   $$
   1.093807 - 1 \approx 0.093807
   $$

5. **Convert to a percentage**:
   $$
   0.093807 \times 100 \approx 9.3807\%
   $$

Rounding this to the nearest tenth of a percent gives us $$ 9.4\% $$.

Thus, the effective annual yield for the passbook savings account is approximately **9.4%**.
The effective annual yield is approximately **9.4%**.

Find the effective annual yield for a passbook savings account that has a rate of \( 9 \% \) compounded monthly, Round the answer to the nearest tenth of a percent. \( .0 .0938 \% \) \( 10.0 \% \) \( 9.0 \% \) \( 9.4 \% \)

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