1. **Problem Statement:** (a) Calculate the total amount to be returned on a loan of 48.52 million at 0.5% simple interest per month after 1.5 years. (b) Calculate the total cost of buying 80 drinkers priced at 21,500 each with discounts: 10% on total cost for every 50 drinkers and an additional 5% on the excess over 50. (c) Estimate the capacity of each drinker shaped as a rectangular prism with a semi-cylindrical top and advise on tank capacity. 2. **Formulas and Rules:** - Simple Interest: $$I = P \times r \times t$$ where $P$ is principal, $r$ is rate per period, $t$ is time in periods. - Total amount: $$A = P + I$$ - Discounts applied sequentially on total cost. - Volume of rectangular prism: $$V_{rect} = l \times w \times h$$ - Volume of semi-cylinder: $$V_{semi} = \frac{1}{2} \pi r^2 h$$ - Total volume = volume of prism + volume of semi-cylinder. 3. **Calculations:** **(a) Loan repayment:** - Principal $P = 48.52$ million - Rate per month $r = 0.5\% = 0.005$ - Time $t = 1.5$ years $= 1.5 \times 12 = 18$ months - Interest $$I = 48.52 \times 0.005 \times 18 = 48.52 \times 0.09 = 4.3668$$ million - Total amount $$A = 48.52 + 4.3668 = 52.8868$$ million **(b) Cost of drinkers:** - Number of drinkers = 80 - Price per drinker = 21,500 - Total cost before discount $$= 80 \times 21500 = 1,720,000$$ - Discount for first 50 drinkers: 10% on total cost - Additional discount for excess 30 drinkers: 5% on total cost - Calculate discounts: - 10% discount: $$0.10 \times 1,720,000 = 172,000$$ - 5% discount: $$0.05 \times 1,720,000 = 86,000$$ - Total discount $$= 172,000 + 86,000 = 258,000$$ - Final cost $$= 1,720,000 - 258,000 = 1,462,000$$ **(c) Capacity of each drinker:** - Dimensions of rectangular prism part: - Length $l = CH = 50$ cm - Width $w = BC = 20$ cm - Height $h = AB = 10$ cm - Volume of prism $$V_{rect} = 50 \times 20 \times 10 = 10,000 \text{ cm}^3$$ - Diameter of semi-circle $AD = AB = 10$ cm, so radius $$r = \frac{10}{2} = 5 \text{ cm}$$ - Height of semi-cylinder (same as width) $$h = BC = 20 \text{ cm}$$ - Volume of semi-cylinder $$V_{semi} = \frac{1}{2} \pi r^2 h = \frac{1}{2} \times \pi \times 5^2 \times 20 = 0.5 \times \pi \times 25 \times 20 = 250\pi \approx 785.4 \text{ cm}^3$$ - Total volume $$V = V_{rect} + V_{semi} = 10,000 + 785.4 = 10,785.4 \text{ cm}^3$$ - Convert to liters (1 liter = 1000 cm³): $$10,785.4 \div 1000 = 10.7854 \text{ liters}$$ **Advice:** - Each drinker holds approximately 10.79 liters. - For 80 drinkers, total capacity needed is $$80 \times 10.7854 = 862.832 \text{ liters}$$. - Recommend a water tank with capacity at least 863 liters to ensure sufficient water supply. **Final answers:** (a) Total repayment: 52.8868 million (b) Total cost of drinkers: 1,462,000 (c) Capacity per drinker: approximately 10.79 liters; recommended tank capacity: at least 863 liters.