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

To determine the interest rate, we can use the formula for compound interest:

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

Where:
- \( A \) is the final amount (41,070),
- \( P \) is the initial investment (27,750),
- \( r \) is the annual interest rate (unknown),
- \( t \) is the time in years (6).

Now, let's solve for \( r \). The formula becomes:

\[
41,070 = 27,750(1 + r)^6
\]

We can isolate \( r \) by following these steps:
1. Divide both sides by 27,750:
\[
\frac{41,070}{27,750} = (1 + r)^6
\]
2. Take the sixth root of both sides to solve for \( 1 + r \):
\[
(1 + r) = \left(\frac{41,070}{27,750}\right)^{\frac{1}{6}}
\]
3. Subtract 1 to isolate \( r \).

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

Would you like further details on how this calculation works, or any clarifications?

Here are 5 related questions to explore:
1. How would the interest rate change if the time period was longer or shorter?
2. What would the balance be if the interest rate was compounded quarterly instead of annually?
3. How much would the final amount be if the interest rate was higher?
4. What would be the effect of continuous compounding on the investment?
5. How does simple interest compare to compound interest in this scenario?

**Tip:** Always check if the interest is compounded annually, quarterly, or continuously, as this affects the final balance.

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

Learn how to calculate the interest rate on an investment of 27,750 that grows to 41,070 over 6 years using the compound interest formula. This example covers key concepts like compound interest, exponential growth, and algebra. Suitable for high school students in Grades 10-12.

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