A bank features a savings account that has an annual percentage rate of $$ 3.4 \% $$ with interest compounded semi-annually. Claire deposits $$ \$ 6,000 $$ into the account. What is the annual percentage yield (APY) for the savings account? APY $$ = $$ (Round to the nearest hundredth of a percent.)

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Let the nominal annual interest rate be $$ r = 0.034 $$. Since the interest is compounded semi-annually, the interest rate per period is

$$
\frac{r}{2} = \frac{0.034}{2} = 0.017.
$$

The effective annual yield is given by the formula

$$
\text{APY} = \left(1 + \frac{r}{2}\right)^2 - 1.
$$

Substitute the value of $$ r $$:

$$
\text{APY} = \left(1 + 0.017\right)^2 - 1 = (1.017)^2 - 1.
$$

Calculating $$ (1.017)^2 $$:

$$
(1.017)^2 \approx 1.034289.
$$

Thus,

$$
\text{APY} \approx 1.034289 - 1 = 0.034289.
$$

To convert this to a percentage, multiply by $$ 100 $$:

$$
\text{APY} \approx 0.034289 \times 100 \approx 3.43\%.
$$

So, the annual percentage yield (APY) is $$ \boxed{3.43\%} $$.
The annual percentage yield (APY) is approximately $$ 3.43\% $$.

A bank features a savings account that has an annual percentage rate of \( 3.4 \% \) with interest compounded semi-annually. Claire deposits \( \$ 6,000 \) into the account. What is the annual percentage yield (APY) for the savings account? APY \( = \) (Round to the nearest hundredth of a percent.)

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