This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the solutions to the questions. Q2. a) Step 1: Calculate the value after the first year. The car depreciates by 20% in the first year. Value after 1st year = shs. 800,000 × (1 - 0.20) = shs. 800,000 × 0.80 = shs. 640,000 Step 2: Calculate the value after the second year. The car depreciates by 5% in the second year. Value after 2nd year = shs. 640,000 × (1 - 0.05) = shs. 640,000 × 0.95 = shs. 608,000 Step 3: Calculate the value after the third, fourth, and fifth years. The car depreciates by 10% for each of these three years. Value after 5th year = shs. 608,000 × (1 - 0.10)^3 = shs. 608,000 × (0.90)^3 Value after 5th year = shs. 608,000 × 0.729 = shs. 443,232 Step 4: Calculate how much less it will cost at the end of the fifth year. Difference = Initial cost - Value after 5th year Difference = shs. 800,000 - shs. 443,232 = shs. 356,768 The car will cost shs. 356,768 less at the end of the fifth year. shs. 356,768 Q2. b) Step 1: Calculate the Simple Interest (SI). The formula for simple interest is SI = P × R × T. Given: Principal (P) = shs. 3,000, Rate (R) = 15% = 0.15, Time (T) = 2 years. SI = shs. 3,000 × 0.15 × 2 = shs. 900 Step 2: Calculate the Compound Interest (CI). The formula for the amount with compound interest is A = P(1 + R)^T. A = shs. 3,000 (1 + 0.15)^2 = shs. 3,000 (1.15)^2 A = shs. 3,000 × 1.3225 = shs. 3,967.50 Compound Interest (CI) is A - P. CI = shs. 3,967.50 - shs. 3,000 = shs. 967.50 Step 3: Find by how much the compound interest will exceed simple interest. Difference = CI - SI = shs. 967.50 - shs. 900 = shs. 67.50 The compound interest will exceed simple interest by shs. 67.50. shs. 67.50 Q3. a) Step 1: Calculate the total amount paid in installments. Joseph pays 24 equal monthly installments of shs. 1,250. Total installments = 24 × shs. 1,250 = shs. 30,000 Step 2: Find the hire purchase price of the camera. The hire purchase price is the sum of the deposit and the total installments. Hire Purchase Price = Deposit + Total installments Hire Purchase Price = shs. 7,200 + shs. 30,000 = shs. 37,200 The hire purchase price of the camera is shs. 37,200. shs. 37,200 Q3. b) Step 1: Set up the relationship between the hire purchase price and the cash price. Let the cash price be C. The hire purchase price (HPP) is 24% higher than the cash price. HPP = C + 0.24C = 1.24C From part (a), we know the HPP is shs. 37,200. Step 2: Calculate the cash price. shs. 37,200 = 1.24C C = shs. 37,2001.24 C = shs. 30,000 The cash price of the camera is shs. 30,000. shs. 30,000 That's 2 down. 3 left today — send the next one.