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The question in the image reads:

**Stanley invests £7500 for 4 years in a savings account. The savings account pays compound interest at a rate of x% per year. At the end of 4 years the investment is worth £7866.53.**

- **Work out the value of x.**
- **Give your answer correct to 1 decimal place.**

---

To solve for \(x\), the formula for compound interest is:

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

Where:
- \(A\) is the final amount (£7866.53),
- \(P\) is the principal (£7500),
- \(r\) is the annual interest rate (which we need to find),
- \(n\) is the number of years (4).

Substitute the values we know:

\[
7866.53 = 7500(1 + \frac{x}{100})^4
\]

### Step 1: Divide both sides by 7500

\[
\frac{7866.53}{7500} = (1 + \frac{x}{100})^4
\]

\[
1.04887067 = (1 + \frac{x}{100})^4
\]

### Step 2: Take the fourth root of both sides

\[
(1.04887067)^{\frac{1}{4}} = 1 + \frac{x}{100}
\]

\[
1.011927 = 1 + \frac{x}{100}
\]

### Step 3: Subtract 1 from both sides

\[
0.011927 = \frac{x}{100}
\]

### Step 4: Multiply by 100

\[
x = 1.1927
\]

### Final Answer:

The interest rate \(x\) is approximately **1.2%** (to 1 decimal place).

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Would you like further details or clarifications?

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Here are 5 related questions to expand on this topic:

1. How would the formula change if the interest were compounded quarterly instead of annually?
2. What would the final amount be if the interest rate was compounded monthly?
3. How does compound interest differ from simple interest in long-term savings?
4. How does the number of compounding periods per year affect the total investment return?
5. What happens to the interest rate if the investment duration is doubled?

**Tip:** When calculating compound interest, the frequency of compounding (annual, quarterly, monthly) significantly impacts the final amount.

Stanley invests £7500 for 4 years in a savings account. The savings account pays compound interest at a rate of x% per year. At the end of 4 years the investment is worth £7866.53. Work out the value of x. Give your answer correct to 1 decimal place.

Learn how to determine the interest rate in a compound interest investment problem. This example involves an investment of £7500 over 4 years, resulting in a final amount of £7866.53. Follow the detailed step-by-step solution to find the interest rate, suitable for Grades 10-12.

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