This business/management problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.
ScanSolve AI Answer
Bontlee, let's knock this out. 2.2.1 Step 1: Identify the term agreement for bond payment option one from Table 4. The term agreement for Option 1 is 10 years. Step 2: Convert the term agreement from years to months. Term in months = 10 years × 12 months/year Term in months = 120 months The term agreement in months for bond payment option one is 120 months. 2.2.2 Step 1: Identify the annual interest rate from Table 4. The annual interest rate is 10.75\%. Step 2: Convert the annual interest rate to a monthly rate. Monthly interest rate = (10.75\%)/(12) Monthly interest rate = (0.1075)/(12) Monthly interest rate ≈ 0.00895833... Step 3: Convert to a percentage and round to one decimal place. Monthly interest rate ≈ 0.00895833... × 100\% Monthly interest rate ≈ 0.895833...\% Monthly interest rate ≈ 0.9\% The interest rate per month, rounded to one decimal place, is 0.9\%. 2.2.3 Step 1: Identify the monthly instalment and once-off costs for Option 1 from Table 4. Monthly instalment (Option 1) = R68 033 Once-off costs (Option 1) = R1 600 015 Step 2: Calculate the total value of monthly instalments for Option 1. The term in months for Option 1 is 120 months (from 2.2.1). Total value of monthly instalments = Monthly instalment × Number of months Total value of monthly instalments = R68\,033 × 120 Total value of monthly instalments = R8\,163\,960 Step 3: Calculate the total cost of the house using the given formula. Total cost = Total value of monthly instalments + Once-off costs Total cost = R8\,163\,960 + R1\,600\,015 Total cost = R9\,763\,975 The total cost of the house if Mpho uses bond payment option one is R9\,763\,975. 2.2.4 Step 1: Identify the purchase price from Table 4. Purchase Price = R5 990 000 Step 2: Calculate the difference between the total cost (from 2.2.3) and the purchase price. Difference = Total cost - Purchase Price Difference = R9\,763\,975 - R5\,990\,000 Difference = R3\,773\,975 Step 3: Calculate the percentage more than the purchase price. Percentage more = DifferencePurchase Price × 100\% Percentage more = R3\,773\,975R5\,990\,000 × 100\% Percentage more ≈ 0.6300459... × 100\% Percentage more ≈ 63.00\% Mpho will be paying approximately 63.00\% more than the purchase price. 2.2.5 & 2.2.6 Step 1: Identify the principal amount, interest rate, and time for the loan. Principal (P) = R350 000 Interest rate (r) = 17% = 0.17 Time (t) = 3 years Step 2: Calculate the total amount Mpho pays back using the simple interest formula A = P(1 + rt). A = R350\,000 (1 + 0.17 × 3) A = R350\,000 (1 + 0.51) A = R350\,000 (1.51) A = R528\,500 Step 3: Round the amount to the nearest one hundred rand. The amount R528 500 is already rounded to the nearest one hundred rand. The amount Mpho pays back, rounded to the nearest one hundred rand, is R528\,500. 2.2.7 Step 1: Calculate the total monthly instalments for Option 2. Term agreement (Option 2) = 15 years = 15 × 12 = 180 months. Monthly instalment (Option 2) = R55 935. Total instalments (Option 2) = R55\,935 × 180 Total instalments (Option 2) = R10\,068\,300 Step 2: Calculate the total monthly instalments for Option 3. Term agreement (Option 3) = 20 years = 20 × 12 = 240 months. Monthly instalment (Option 3) = R50 659. Total instalments (Option 3) = R50\,659 × 240 Total instalments (Option 3) = R12\,158\,160 Step 3: Calculate the difference between the total monthly instalments of Option 2 and Option 3. Difference = |Total instalments (Option 2) - Total instalments (Option 3)| Difference = |R10\,068\,300 - R12\,158\,160| Difference = |-R2\,089\,860| Difference = R2\,089\,860 Step 4: Verify Mpho's statement. Mpho stated that the difference is less than R2 000 000. Our calculated difference is R2 089 860. Since R2 089 860 is not less than R2 000 000 (it is greater), Mpho's statement is invalid. Mpho's statement is invalid. What's next?