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
Step 1: Identify the given values. Principal amount P = R10\,000 Interest rate i = 11\% = 0.11 Number of years n = 3 Step 2: Calculate the future value using the compound interest formula. The formula for compound interest is A = P(1 + i)^n. A = R10\,000(1 + 0.11)^3 A = R10\,000(1.11)^3 A = R10\,000(1.367631) A = R13\,676.31 Step 3: Calculate the profit. Profit = Future Value - Principal Amount Profit = A - P Profit = R13\,676.31 - R10\,000 Profit = R3\,676.31 The profit Roxanne will have is R3\,676.31. 4.1 His monthly instalment over the 3-year period. Step 1: Calculate the deposit amount. Laptop price = R3 999 Deposit percentage = 15% Deposit = 0.15 × R3\,999 Deposit = R599.85 Step 2: Calculate the amount to be financed. Amount financed = Laptop price - Deposit Amount financed = R3\,999 - R599.85 Amount financed = R3\,399.15 Step 3: Determine the monthly interest rate and number of payments. Annual interest rate i_annual = 18\% = 0.18 Monthly interest rate i_monthly = (0.18)/(12) = 0.015 Number of years n_years = 3 Number of months n_months = 3 × 12 = 36 Step 4: Calculate the monthly instalment for the financed amount using the present value annuity formula. The formula for the present value of an annuity is P = x[1 - (1 + i)^-n]i, where P is the present value (amount financed), x is the monthly instalment, i is the monthly interest rate, and n is the number of months. Solving for x: x = (P · i)/(1 - (1 + i)^-n) x = R3\,399.15 × 0.0151 - (1 + 0.015)^-36 x = (50.98725)/(1 - (1.015)^-36) x = (50.98725)/(1 - 0.58509836) x = (50.98725)/(0.41490164) x ≈ R122.89 This is the monthly instalment for the loan repayment. Step 5: Add the monthly insurance fee to find the total monthly instalment. Monthly insurance fee = R30 Total monthly instalment = Loan instalment + Insurance fee Total monthly instalment = R122.89 + R30 Total monthly instalment = R152.89 His monthly instalment is R152.89. **4.2 The total amount he will have paid at the end