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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Step 1: Answer Question 5.1. Compound interest leads to faster appreciation because the interest earned in each period is added to the principal, and subsequent interest is calculated on this larger amount. This creates an accelerating growth effect. Step 2: Solve Question 5.2. The formula for simple interest is A = P(1 + i · n). Given: A = R22\,464, i = 5.5\% = 0.055, n = 8 years. We need to find P. 22\,464 = P(1 + 0.055 × 8) 22\,464 = P(1 + 0.44) 22\,464 = P(1.44) P = (22\,464)/(1.44) P = 15\,600 The initial investment was R15 600. Step 3: Solve Question 5.3.1. The formula for compound interest compounded quarterly is A = P(1 + (i)/(m))^n · m. Given: P = R17\,500, i = 7.5\% = 0.075, n = 12 years, m = 4 (quarterly). A = 17\,500 (1 + (0.075)/(4))^12 × 4 A = 17\,500 (1 + 0.01875)^48 A = 17\,500 (1.01875)^48 A = 17\,500 × 2.450659... A = 42\,886.53 The amount of her investment after 12 years is R42 886.53. Step 4: Solve Question 5.3.2. The interest earned is the final amount minus the initial principal. I = A - P I = R42\,886.53 - R17\,500 I = R25\,386.53 The interest her investment would earn is R25 386.53. Step 5: Solve Question 5.4. First, calculate the depreciated value of the old car. The formula for reducing balance depreciation is A = P(1 - i)^n. Given: P = R350\,000, i = 20\% = 0.20, n = 7 years. A_old = 350\,000 (1 - 0.20)^7 A_old = 350\,000 (0.80)^7 A_old = 350\,000 × 0.2097152 A_old = R73\,400.32 Next, calculate the appreciated value of the new car. The formula for simple interest appreciation is A = P(1 + i · n). Given: P = R350\,000, i = 5\% = 0.05, n = 7 years. A_new = 350\,000 (1 + 0.05 × 7) A_new = 350\,000 (1 + 0.35) A_new = 350\,000 (1.35) A_new = R472\,500 Finally, calculate the amount Musi will pay. Amount to pay = A_new - A_old Amount to pay = R472\,500 - R73\,400.32 Amount to pay = R399\,099.68 Musi will pay R399 099.68. Step 6: Define Question 5.5.1. Taxable income is the portion of an individual's or company's gross income that is subject to income tax. It is calculated by subtracting allowable deductions from gross income. Step 7: Define Question 5.5.2. A tax rebate is an amount by which a taxpayer's tax liability is reduced. It directly lowers the amount of tax owed, rather than reducing the taxable income. Step 8: Solve Question 5.6. First, calculate Mary's total annual gross income. Gross annual salary = R150\,000 × 12 = R1\,800\,000 Total annual gross income = Gross annual salary + 13th cheque + Annual performance bonus Total annual gross income = R1\,800\,000 + R100\,000 + R75\,000 Total annual gross income = R1\,975\,000 This is Mary's taxable income, assuming no other deductions. To calculate Mary's actual tax liability and determine if she overpaid or underpaid, the individual tax rate table for the financial year 2024 from SARS is required. This table is not provided in the image. Without the tax brackets, rates, and applicable rebates for a 70-year-old, the final tax calculation cannot be completed. Her total annual taxable income is R1 975 000. Send me the next one 📸