1. The problem is to understand the formula for compound interest and how it relates to the given table. 2. The formula for compound interest is: $$A = P \times (1 + r)^n$$ where: - $A$ is the amount of money accumulated after $n$ years, including interest. - $P$ is the principal amount (initial money). - $r$ is the annual interest rate (in decimal). - $n$ is the number of years. 3. From the table: - Start: £500.00 (this is $P$) - After 1 year: £520.00 - After 2 years: £540.80 4. Calculate the interest rate $r$ using the first year data: $$520 = 500 \times (1 + r)^1$$ Divide both sides by 500: $$\frac{520}{500} = \cancel{\frac{500}{500}} \times (1 + r)$$ $$1.04 = 1 + r$$ So, $$r = 1.04 - 1 = 0.04$$ which is 4% annual interest. 5. Verify the amount after 2 years: $$A = 500 \times (1.04)^2 = 500 \times 1.0816 = 540.8$$ which matches the table. 6. Therefore, the formula for the amount after $n$ years is: $$A = 500 \times (1.04)^n$$ where $A$ is the amount after $n$ years, $500$ is the initial amount, and $1.04$ represents the growth factor (1 + 4% interest rate).