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.