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.
ScanSolve AI Answer
Welcome back General — missed you this week. Here are the solutions to question 2: a) The value of her car in January 2025. Step 1: Identify the initial value, depreciation rate, and time period. The initial value of the car in January 2022 is Shs 12,500,000. The depreciation rate is 10\% per annum. The time period from January 2022 to January 2025 is 3 years. Step 2: Apply the depreciation formula. The formula for depreciation is A = P(1 - r)^n, where A is the final value, P is the initial value, r is the depreciation rate, and n is the number of years. A = 12,500,000(1 - 0.10)^3 A = 12,500,000(0.90)^3 A = 12,500,000 × 0.729 A = 9,112,500 The value of her car in January 2025 is Shs 9,112,500. b) The amount she will pay if she buys the car by paying cash. Step 1: Identify the new car price and discount rate. The brand new car costs Shs 24,000,000. The cash payment option offers an 8\% discount. Step 2: Calculate the discount amount. Discount = 8\% × 24,000,000 Discount = 0.08 × 24,000,000 Discount = 1,920,000 Step 3: Calculate the amount to pay after the discount. Amount to pay = New car price - Discount Amount to pay = 24,000,000 - 1,920,000 Amount to pay = 22,080,000 The amount she will pay if she buys the car by paying cash is Shs 22,080,000. c) The saving she would make if she bought the car by paying cash rather than paying in installments. Step 1: Calculate the total cost for the installment option. The installment option requires a 60\% deposit of the cash value and then Shs 5,000,000 per month for 3 months. Deposit = 60\% × 24,000,000 Deposit = 0.60 × 24,000,000 Deposit = 14,400,000 Total monthly payments = 5,000,000 × 3 Total monthly payments = 15,000,000 Total installment cost = Deposit + Total monthly payments Total installment cost = 14,400,000 + 15,000,000 Total installment cost = 29,400,000 Step 2: Calculate the saving. The cash payment amount from part b) is Shs 22,080,000. Saving = Total installment cost - Cash payment amount Saving = 29,400,000 - 22,080,000 Saving = 7,320,000 The saving she would make if she bought the car by paying cash rather than paying in installments is Shs 7,320,000. d) How much more money does she need to top on the value of the old car to accomplish the deposit of the new car under the second option of payment. Step 1: Identify the value of the old car and the required deposit. The value of the old car in January 2025 from part a) is Shs 9,112,500. The deposit for the new car under the second option is Shs 14,400,000 (calculated in part c). Step 2: Calculate the additional money needed. Money needed to top up = Required deposit - Value of old car Money needed to top up = 14,400,000 - 9,112,500 Money needed to top up = 5,287,500 She needs to top up Shs 5,287,500 more. Send me the next one 📸