Use the compound interest formula Aequals​P(1plus​r)Superscript t and the given information to solve for r.
Aequals​$2600​, Pequals​$1700​, tequals6

Do not simplify

To solve for the rate $ r $ using the compound interest formula:

\[
A = P(1 + r)^t
\]

Given:
- $ A = 2600 $
- $ P = 1700 $
- $ t = 6 $

We substitute these values into the formula:

\[
2600 = 1700(1 + r)^6
\]

Next, solve for $ r $ step by step.

1. Divide both sides of the equation by 1700:

\[
\frac{2600}{1700} = (1 + r)^6
\]

2. Simplify the fraction on the left-hand side:

\[
\frac{2600}{1700} = \frac{26}{17}
\]

Thus, the equation becomes:

\[
\frac{26}{17} = (1 + r)^6
\]

At this point, you would take the 6th root of both sides to isolate $ 1 + r $, and then solve for $ r $, but since you requested not to simplify, we'll leave the equation in this form:

\[
r = \left( \frac{26}{17} \right)^{\frac{1}{6}} - 1
\]

Do you want to proceed with simplifying, or do you have any questions about this step?

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Here are 5 related questions that expand on this information:

1. How would you calculate the final value of $ r $ by simplifying the equation?
2. What is the impact of changing the time period $ t $ on the interest rate $ r $?
3. How would the formula change if the interest was compounded monthly instead of annually?
4. Can you calculate the value of $ r $ using logarithms to avoid roots?
5. How would you use this formula to calculate future investment returns with a known interest rate?

**Tip:** Compound interest calculations are sensitive to both the rate and the time period. Small changes in either can have a large effect on the final amount.

Use the compound interest formula A = P(1 + r)^t and the given information to solve for r. A = $2600, P = $1700, t = 6. Do not simplify.

Learn how to solve for the interest rate (r) using the compound interest formula A = P(1 + r)^t with the given values A = 2600, P = 1700, and t = 6. This problem covers algebraic concepts related to exponential equations and compound interest. Suitable for students in Grades 9-12.

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