1. **State the problem:** We are given the amount owed on a loan at the end of 2002 (£427.33) and at the end of 2007 (£592.39). We want to find the interest gathered over the next 3 years after 2007. 2. **Recall the compound interest formula:** $$A = P(1 + r)^t$$ where $A$ is the amount after $t$ years, $P$ is the principal, $r$ is the annual interest rate, and $t$ is time in years. 3. **Find the interest rate $r$ using the data from 2002 to 2007 (5 years):** $$592.39 = 427.33(1 + r)^5$$ Divide both sides by 427.33: $$\frac{592.39}{427.33} = (1 + r)^5$$ Calculate the left side: $$1.3869 = (1 + r)^5$$ Take the 5th root: $$1 + r = \sqrt[5]{1.3869}$$ Calculate: $$1 + r \approx 1.068 \Rightarrow r \approx 0.068$$ So, the annual interest rate is approximately 6.8%. 4. **Calculate the amount owed after the next 3 years (2007 to 2010):** $$A = 592.39(1 + 0.068)^3$$ Calculate: $$A = 592.39 \times 1.068^3 = 592.39 \times 1.2187 \approx 721.56$$ 5. **Calculate the interest gathered over these 3 years:** $$\text{Interest} = 721.56 - 592.39 = 129.17$$ **Final answer:** The loan gathered approximately 129.17 in interest over the next 3 years.