$$ P $$ 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 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 $$ 8.5 \% $$. Part: $$ \mathbf{1 / 3} $$ Part 2 of 3 (b) In another account $$ \$ 10,000 $$ grows to $$ \$ 25,579 $$ after 7 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 $$ r $$ for the second account where $$ P = 10,000 $$, $$ A = 25,579 $$, and $$ t = 7 $$, we can use the formula:

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

Substituting the values into the formula:

$$
r = \left(\frac{25,579}{10,000}\right)^{\frac{1}{7}} - 1
$$

Calculating $$ \frac{25,579}{10,000} $$:

$$
\frac{25,579}{10,000} = 2.5579
$$

Now, we take the seventh root of $$ 2.5579 $$:

$$
r = (2.5579)^{\frac{1}{7}} - 1
$$

Using a calculator to find $$ (2.5579)^{\frac{1}{7}} $$:

$$
(2.5579)^{\frac{1}{7}} \approx 1.3034
$$

Now, subtract 1:

$$
r \approx 1.3034 - 1 = 0.3034
$$

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

$$
r \approx 0.3034 \times 100 \approx 30.34\%
$$

Rounding to the nearest tenth of a percent:

$$
r \approx 30.3\%
$$

Thus, the interest rate is approximately $$ \boxed{30.3} \% $$.30.3%

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