1. **Problem statement:** (a) Determine which carton size of Smiley Orange Juice is the better buy based on cost per ml. (c) Faye borrowed 9600 at 8% compound interest. (i) Calculate the interest for the first year. (ii) Calculate the remaining loan after repaying 4368 at the end of the first year. (iii) Calculate the interest on the remaining balance for the second year. --- 2. **Formulas and rules:** - Cost per ml = \( \frac{\text{Cost}}{\text{Volume}} \) - Compound interest for one year = \( \text{Principal} \times \text{Rate} \) - Remaining balance after repayment = \( \text{Principal} + \text{Interest} - \text{Repayment} \) --- 3. **Solution for (a):** - For 350 ml carton: \( \frac{4.20}{350} = 0.012 \) per ml - For 450 ml carton: \( \frac{5.13}{450} \approx 0.0114 \) per ml Since 0.0114 < 0.012, the 450 ml carton is the better buy because it costs less per ml. --- 4. **Solution for (c)(i):** - Interest for first year = \( 9600 \times 0.08 = 768 \) --- 5. **Solution for (c)(ii):** - Amount owed at start of second year = Principal + Interest - Repayment - \( 9600 + 768 - 4368 = 6000 \) --- 6. **Solution for (c)(iii):** - Interest on remaining balance for second year = \( 6000 \times 0.08 = 480 \) --- **Final answers:** - (a) The 450 ml carton is the better buy. - (c)(i) Interest for first year = 768 - (c)(ii) Amount owed at start of second year = 6000 - (c)(iii) Interest for second year = 480