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
Morning Sephybwoy — let's get this done. Here's how to solve the problem: Step 1: Determine the loan amount. The loan amount is the cash price minus the deposit. Loan Amount (PV) = Cash Price - Deposit PV = Sh. 24,600 - Sh. 10,200 PV = Sh. 14,400 Step 2: Calculate the amount paid for each installment. We use the present value of an annuity formula to find the monthly installment (PMT). The formula is: PV = PMT × 1 - (1 + r)^-nr Rearranging to solve for PMT: PMT = PV × (r)/(1 - (1 + r)^-n) Given: PV = Sh. 14,400 r = 2.1\% per month = 0.021 n = 18 months Substitute the values into the formula: PMT = 14,400 × (0.021)/(1 - (1 + 0.021)^-18) PMT = 14,400 × (0.021)/(1 - (1.021)^-18) Calculate (1.021)^-18: (1.021)^-18 ≈ 0.690596608 Now substitute this back: PMT = 14,400 × (0.021)/(1 - 0.690596608) PMT = 14,400 × (0.021)/(0.309403392) PMT = 14,400 × 0.067869600 PMT ≈ Sh. 977.32 a) The amount paid for each installment is: Sh. 977.32 Step 3: Calculate the total amount paid. The total amount paid is the sum of the deposit and all installments. Total Amount Paid = Deposit + (Number of Installments × Amount per Installment) Total Amount Paid = Sh. 10,200 + (18 × Sh. 977.32) Total Amount Paid = Sh. 10,200 + Sh. 17,591.76 Total Amount Paid = Sh. 27,791.76 b) The total amount paid is: Sh. 27,791.76 Send me the next one 📸