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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Here are the solutions to your questions: 1.1 Give an example of, or a word for, each of the following terms: 1.1.1 Fixed income: Salary or Pension* 1.1.2 Medium-term investment: Fixed deposit* (e.g., 1-5 years) 1.1.3 A money lender who lends out money for profit: Bank or Moneylender* 1.1.4 The difference between the budgeted amount and the actual amount: Variance* 1.1.5 Long-term investment: Property or Shares* 1.2 Pinkie buys a laptop priced at R13 495. She takes out a 12-month hire-purchase agreement. She pays a deposit of 20% and the interest charged on the balance is 15% per annum simple interest. 1.2.1 What will she actually pay for the laptop? Step 1: Calculate the deposit amount. Deposit = 20\% × R13\,495 = 0.20 × R13\,495 = R2\,699 Step 2: Calculate the balance to be financed. Balance = R13\,495 - R2\,699 = R10\,796 Step 3: Calculate the simple interest on the balance for 12 months (1 year). The simple interest formula is I = P · r · t. I = R10\,796 × 0.15 × 1 = R1\,619.40 Step 4: Calculate the total amount to be repaid on the loan. Amount to repay = Balance + Interest = R10\,796 + R1\,619.40 = R12\,415.40 Step 5: Calculate the total amount Pinkie will pay for the laptop. Total paid = Deposit + Amount to repay = R2\,699 + R12\,415.40 = R15\,114.40 Pinkie will actually pay for the laptop: R15\,114.40 1.2.2 What will her monthly payment be? Step 1: Use the total amount to be repaid on the loan from 1.2.1 and divide by the number of months. Monthly payment = R12\,415.4012 = R1\,034.62 Her monthly payment will be: R1\,034.62 1.3 Themba won R 5 400 in a talent show. He was given two options to invest this money. OPTION A: for 3 years @ 6,4% compound interest, compounded annually OPTION B: for 3 years @ 7% simple interest. Which option should he choose? Give a reason for your answer and show ALL calculations. Step 1: Calculate the future value for Option A (Compound Interest). The formula for compound interest is A = P(1 + i)^n. A_A = R5\,400(1 + 0.064)^3 A_A = R5\,400(1.064)^3 A_A = R5\,400(1.204161) A_A = R6\,499.47 Step 2: Calculate the future value for Option B (Simple Interest). The formula for simple interest is A = P(1 + r · t). A_B = R5\,400(1 + 0.07 × 3) A_B = R5\,400(1 + 0.21) A_B = R5\,400(1.21) A_B = R6\,534 Step 3: Compare the two options and make a choice. Option A yields R6 499.47. Option B yields R6 534. Themba should choose Option B because it yields a higher return. Themba should choose: Option B Reason: Option B yields a higher return of R6 534 compared to Option A's R6 499.47. 1.4 An amount of R1 200 accumulates to R2 600 after 3 years. Find the interest rate if the investment earned compound interest, compounded annually. Step 1: Write down the compound interest formula and substitute the given values. The formula for compound interest is A = P(1 + i)^n. R2\,600 = R1\,200(1 + i)^3 Step 2: Isolate the term (1 + i)^3. (2\,600)/(1\,200) = (1 + i)^3 (26)/(12) = (1 + i)^3 (13)/(6) = (1 + i)^3 2.16666... = (1 + i)^3 Step 3: Take the cube root of both sides. [3]2.16666... = 1 + i 1.29386... = 1 + i Step 4: Solve for i and convert to a percentage. i = 1.29386... - 1 i = 0.29386... i ≈ 29.39\% The interest rate is: 29.39\% Send me the next one 📸