What what's the interest rate if your balance on an investment of 27 750 at the end of six years is 41 070

To find the interest rate on an investment, we can use the formula for compound interest or simple interest. Since the problem does not specify, I'll assume it's compound interest, which is the more common scenario for investments.

The formula for compound interest is:

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

Where:
- $A$ is the final amount (41,070),
- $P$ is the principal amount (27,750),
- $r$ is the annual interest rate (in decimal form),
- $t$ is the time the money is invested (6 years).

We need to solve for $r$. Let's rearrange the formula:

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

Now, let's calculate it:

\[
r = \left( \frac{41,070}{27,750} \right)^{\frac{1}{6}} - 1
\] 

I'll calculate this now.The annual interest rate is approximately 6.75%.

Would you like more details or have any questions?

Here are five related questions to expand your understanding:

1. How would the interest rate change if the investment period was longer?
2. What would the interest rate be for simple interest instead of compound interest?
3. How can you calculate the total amount of interest earned over the 6 years?
4. What if the interest compounds monthly instead of annually?
5. How can you find the interest rate if only part of the final amount is known?

**Tip:** For compound interest, the frequency of compounding (annually, monthly, etc.) can significantly affect the final balance.

What what's the interest rate if your balance on an investment of 27 750 at the end of six years is 41 070?

Calculate the interest rate for an investment of $27,750 that grows to $41,070 over six years using the compound interest formula. This problem involves algebraic concepts and exponents, suitable for high school students in Grades 9-12.

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