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.
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Question 1 1.1 Calculate the amount that Tumi will be able to invest in the bank, if he is going to invest the total amount he has set aside. Step 1: Calculate the total number of months Tumi saved. Number of months = 2 years × 12 months/year = 24 months Step 2: Calculate the total amount Tumi saved. Total saved = R800/month × 24 months = R19\,200 The amount Tumi will be able to invest is R19\,200. 1.2 Determine the Interest he will earn from the bank. Step 1: Identify the principal amount, interest rate, and time. Principal (P) = R19 200 Interest rate (i) = 12.5% p.a. = 0.125 Time (n) = 36 months = (36)/(12) years = 3 years Step 2: Calculate the simple interest using the formula I = P × i × n. I = R19\,200 × 0.125 × 3 = R7\,200 The interest Tumi will earn is R7\,200. 1.3 What is the total amount that he will receive at the end of the investment period? Step 1: Calculate the total amount by adding the principal and the interest. Total amount = Principal + Interest Total amount = R19\,200 + R7\,200 = R26\,400 The total amount Tumi will receive is R26\,400. Question 2 2.1 Calculate how much Tumi had to put down as a deposit for the house. Step 1: Calculate the deposit amount, which is 11.5% of the house price. Deposit = 11.5\% × R549\,000 Deposit = 0.115 × R549\,000 = R63\,135 The deposit for the house is R63\,135. 2.2 If Tumi uses the money he received from the bank at the end of his investment term, will he have enough to pay for the deposit? Show by means of calculations. Step 1: Compare the amount received from the bank with the deposit amount. Amount received from bank = R26 400 Deposit required = R63 135 Step 2: Determine if the amount received is enough. Since R26\,400 < R63\,135, Tumi will not have enough money to pay for the deposit using only the investment. Tumi will need an additional amount of: R63\,135 - R26\,400 = R36\,735 No, Tumi will not have enough money for the deposit. 2.3 Tumi learns that he will have to pay a monthly instalment of R5 380 over a period of 20 years. 2.3.1 If the interest rate does not change, Show with calculations that the total amount paid, including the deposit will be R1 354 335. Step 1: Calculate the total number of months for the instalments. Number of months = 20 years × 12 months/year = 240 months Step 2: Calculate the total amount paid in instalments. Total instalments = R5\,380/month × 240 months = R1\,291\,200 Step 3: Calculate the total amount paid, including the deposit. Total amount paid = Total instalments + Deposit Total amount paid = R1\,291\,200 + R63\,135 = R1\,354\,335 The total amount paid, including the deposit, is indeed R1\,354\,335. 2.3.2 How much more money would Tumi have paid by the end of the 20 years? Step 1: Calculate the difference between the total amount paid and the original house price. More money paid = Total amount paid - House price More money paid = R1\,354\,335 - R549\,000 = R805\,335 Tumi would have paid R805\,335 more. 2.3.3 Calculate the percentage interest that Tumi would have paid by the end of 20 years if the monthly instalment did not change. Round your answer off to one decimal place. Step 1: Determine the actual loan amount. Loan amount = House price - Deposit Loan amount = R549\,000 - R63\,135 = R485\,865 Step 2: Calculate the total interest paid on the loan. Total interest on loan = Total instalments - Loan amount Total interest on loan = R1\,291\,200 - R485\,865 = R805\,335 Step 3: Calculate the percentage interest relative to the loan amount. Percentage interest = Total interest on loanLoan amount × 100\% Percentage interest = R805\,335R485\,865 × 100\% Percentage interest ≈ 1.657409 × 100\% ≈ 165.74\% Step 4: Round the answer to one decimal place. Percentage interest ≈ 165.7\% The percentage interest Tumi would have paid is approximately 165.7\%. That's 2 down. 3 left today — send the next one.