$$ P $$ dollars in principal grows to $$ A $$ dollars after $$ t $$ years with annual interest, then the interest rate is given by $$ r=\left(\frac{A}{P}\right)^{\frac{1}{t}}-1 $$. Part: $$ \mathbf{0 / 3} $$ $$ \square $$ Part 1 of 3 (a) In one account, $$ \$ 10,000 $$ grows to $$ \$ 16,296 $$ after 6 yr. Compute the interest rate. Round your answer to a tenth of a percent. The interest rate is approximately $$ \square $$ \%.

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To find the interest rate $$ r $$, we can use the formula provided:

$$
r = \left(\frac{A}{P}\right)^{\frac{1}{t}} - 1
$$

Where:
- $$ P = 10,000 $$ (the principal)
- $$ A = 16,296 $$ (the amount after 6 years)
- $$ t = 6 $$ (the number of years)

First, we calculate $$ \frac{A}{P} $$:

$$
\frac{A}{P} = \frac{16,296}{10,000} = 1.6296
$$

Next, we substitute this value into the formula for $$ r $$:

$$
r = \left(1.6296\right)^{\frac{1}{6}} - 1
$$

Now we calculate $$ \left(1.6296\right)^{\frac{1}{6}} $$:

Using a calculator, we find:

$$
\left(1.6296\right)^{\frac{1}{6}} \approx 1.085
$$

Now, we can find $$ r $$:

$$
r \approx 1.085 - 1 = 0.085
$$

To express $$ r $$ as a percentage, we multiply by 100:

$$
r \approx 0.085 \times 100 = 8.5\%
$$

Thus, the interest rate is approximately:

$$
\boxed{8.5}
$$8.5%

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