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 Charmaine — missed you this week. Here are the calculations for the deposit and monthly instalments: 1. Calculate the deposit amount. Step 1: Identify the cost of the tractor and the deposit percentage. The tractor costs R 750 000. The deposit is 15% of the tractor cost. Step 2: Calculate the deposit amount. Deposit amount = 15\% × R 750\,000 Deposit amount = 0.15 × 750\,000 Deposit amount = R 112\,500 The deposit amount is R 112\,500. 2. Determine his monthly instalments. Step 1: Calculate the loan amount. The loan amount is the tractor cost minus the deposit. Loan amount = R 750\,000 - R 112\,500 Loan amount = R 637\,500 Step 2: Determine the monthly interest rate and total number of payments. Annual interest rate (r) = 8.6% = 0.086 Compounded monthly, so the monthly interest rate (i) is: i = (r)/(12) = (0.086)/(12) Loan period = 10 years Total number of payments (n) = 10 years × 12 months/year = 120 months Step 3: Use the present value of an annuity formula to find the monthly instalment (x). The formula is: P = x[1 - (1 + i)^-n]i Rearrange to solve for x: x = (P · i)/(1 - (1 + i)^-n) Substitute the values: P = R 637\,500, i = (0.086)/(12), n = 120. x = (637\,500 × 0.086)/(12)1 - (1 + (0.086)/(12))^-120 x = (637\,500 × 0.00716666666...)/(1 - (1.00716666666...)^-120) x = (4562.5)/(1 - 0.420697902...) x = (4562.5)/(0.579302098...) x ≈ 7876.00000... Rounding to two decimal places for currency: x = R 7876.00 His monthly instalments will be R 7876.00. Send me the next one 📸