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 above 50. (c) Estimate the capacity of each drinker shaped as a rectangular prism ABCD E F G H with a semi-circular end ADE, given dimensions AB=10cm, BC=20cm, CH=50cm. 2. **Formulas and rules:** - Simple interest: $$I = P \times r \times t$$ where $P$ is principal, $r$ is monthly rate, $t$ is time in months. - Total amount: $$A = P + I$$ - Discount on total cost: apply percentage discounts sequentially. - Volume of rectangular prism: $$V_{rect} = length \times width \times height$$ - Volume of semi-cylinder (semi-circle base extruded along length): $$V_{semi} = \frac{1}{2} \pi r^2 \times length$$ 3. **Calculations:** (a) Interest and total amount: - Principal $P = 48.52$ million - Rate $r = 0.5\% = 0.005$ per month - Time $t = 1.5$ years $= 1.5 \times 12 = 18$ months Calculate 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: - Price per drinker = 21,500 - Number of drinkers = 80 Calculate total cost before discount: $$Total = 80 \times 21500 = 1,720,000$$ Discounts: - For first 50 drinkers: 10% discount on total cost for 50 drinkers - Excess drinkers = 80 - 50 = 30 Calculate cost for first 50: $$Cost_{50} = 50 \times 21500 = 1,075,000$$ Apply 10% discount: $$Discount_{10\%} = 0.10 \times 1,075,000 = 107,500$$ Cost after discount: $$Cost_{50,disc} = 1,075,000 - 107,500 = 967,500$$ Calculate cost for excess 30: $$Cost_{30} = 30 \times 21500 = 645,000$$ Apply 5% discount: $$Discount_{5\%} = 0.05 \times 645,000 = 32,250$$ Cost after discount: $$Cost_{30,disc} = 645,000 - 32,250 = 612,750$$ Total cost after discounts: $$Total_{disc} = 967,500 + 612,750 = 1,580,250$$ (c) Capacity of each drinker: - Rectangular prism volume: $$V_{rect} = length \times width \times height = 50 \times 10 \times 20 = 10,000 \text{ cm}^3$$ - Semi-circle radius: $$r = \frac{AD}{2} = \frac{10}{2} = 5 \text{ cm}$$ - Volume of semi-cylinder: $$V_{semi} = \frac{1}{2} \pi r^2 \times height = \frac{1}{2} \times \pi \times 5^2 \times 20 = \frac{1}{2} \times \pi \times 25 \times 20 = 250\pi \approx 785.4 \text{ cm}^3$$ - Total volume (capacity) of drinker: $$V = V_{rect} + V_{semi} = 10,000 + 785.4 = 10,785.4 \text{ cm}^3$$ Convert to liters (1 liter = 1000 cm³): $$Capacity = \frac{10,785.4}{1000} = 10.7854 \text{ liters}$$ **Advice:** Since each drinker holds about 10.8 liters, for 80 drinkers total water capacity needed is: $$80 \times 10.7854 = 862.832 \text{ liters}$$ Your neighbor should buy a water tank with capacity at least 863 liters to ensure enough water for all drinkers.