1. **State the problem:** We need to find the value of a loan 10 years after it starts, given its value at the start and after 1 and 2 years. 2. **Identify the type of growth:** The loan value appears to grow exponentially because the increase is not constant but proportional. 3. **Use the exponential growth formula:** $$ V = V_0 \times (1 + r)^t $$ where $V$ is the value after $t$ years, $V_0$ is the initial value, and $r$ is the annual growth rate. 4. **Calculate the growth rate $r$:** Given: $$ V_0 = 7500 $$ $$ V_1 = 7965 $$ Use the formula for $t=1$: $$ 7965 = 7500 \times (1 + r) $$ Solve for $r$: $$ 1 + r = \frac{7965}{7500} = 1.062 $$ $$ r = 0.062 $$ (or 6.2% per year) 5. **Verify with year 2 data:** $$ V_2 = 7500 \times (1.062)^2 = 7500 \times 1.127844 = 8458.83 $$ This matches the given data, confirming $r$. 6. **Calculate the value after 10 years:** $$ V_{10} = 7500 \times (1.062)^{10} $$ Calculate: $$ (1.062)^{10} \approx 1.8194 $$ So: $$ V_{10} = 7500 \times 1.8194 = 13645.5 $$ 7. **Round to nearest penny:** $$ 13645.50 $$ **Final answer:** The value of the loan after 10 years is **13645.50** pounds.