1. **State the problem:** We want to find the values of $A$ and $B$ in the expression $$A \times B^n$$ that models the amount of money in a savings account after $n$ years, given compound interest at 5% per annum. 2. **Given data:** - Initial amount (start): £600.00 - After 1 year: £630.00 - After 2 years: £661.50 3. **Formula for compound interest:** $$\text{Amount after } n \text{ years} = A \times B^n$$ where: - $A$ is the initial amount (principal) - $B$ is the growth factor per year 4. **Find $A$:** Since $n=0$ at the start, the amount is $A \times B^0 = A \times 1 = A$. Therefore, $A = 600$. 5. **Find $B$:** After 1 year ($n=1$), amount is $630$. Using the formula: $$630 = 600 \times B^1 = 600B$$ Divide both sides by 600: $$B = \frac{630}{600} = 1.05$$ 6. **Check with 2 years:** After 2 years ($n=2$), amount is $661.50$. Calculate using $A=600$ and $B=1.05$: $$600 \times (1.05)^2 = 600 \times 1.1025 = 661.5$$ This matches the given data, confirming our values. **Final answer:** $$A = 600, \quad B = 1.05$$