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The problem involves compound interest, and we need to find the interest rate \( x \% \).

The formula for compound interest is:

\[
A = P \left( 1 + \frac{r}{100} \right)^t
\]

Where:
- \( A \) is the final amount (£8029.35),
- \( P \) is the principal amount (£6000),
- \( r \) is the interest rate (which is \( x \% \)),
- \( t \) is the time in years (5 years).

Substituting the given values into the formula:

\[
8029.35 = 6000 \left( 1 + \frac{x}{100} \right)^5
\]

Now, we will solve for \( x \):

1. Divide both sides by 6000:
\[
\frac{8029.35}{6000} = \left( 1 + \frac{x}{100} \right)^5
\]
\[
1.338225 = \left( 1 + \frac{x}{100} \right)^5
\]

2. Take the fifth root of both sides:
\[
1 + \frac{x}{100} = \sqrt[5]{1.338225}
\]
\[
1 + \frac{x}{100} \approx 1.059
\]

3. Subtract 1 from both sides:
\[
\frac{x}{100} = 0.059
\]

4. Multiply by 100:
\[
x = 5.9
\]

Thus, the interest rate \( x \% \) is approximately **5.9\%**.

Would you like further details on the steps? 

Here are 5 related questions for further practice:
1. How would the result change if the investment duration was 10 years instead of 5?
2. What would be the future value of the investment with an interest rate of 7% over 5 years?
3. How can we calculate the monthly compound interest instead of yearly?
4. What happens if the principal amount is increased to £10,000 for the same interest rate and time period?
5. How would the formula change if the interest was compounded quarterly instead of annually?

**Tip:** When solving compound interest problems, always make sure to correctly match the compounding period with the interest rate's time frame.

Naoby invests £6000 for 5 years. The investment gets compound interest of x% per annum. At the end of 5 years the investment is worth £8029.35. Work out the value of x.

This problem covers how to calculate the compound interest rate for a £6000 investment over 5 years, given that the final amount is £8029.35. Using the compound interest formula, we solve for the interest rate x% per annum.

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