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 Question 2 and Question 3. Question 2 2.1 Step 1: Identify the principal amount, interest rate, and time. Principal (P) = R15 000 Annual simple interest rate (r) = 6% = 0.06 Time (t) = 1 year Step 2: Use the simple interest formula I = P · r · t to calculate the interest added each year. I = R15000 × 0.06 × 1 I = R900 The interest that will be added each year is R900. 2.2 Step 1: Identify the principal amount, annual simple interest rate, and total time. Principal (P) = R15 000 Annual simple interest rate (r) = 6% = 0.06 Time (t) = 2 years Step 2: Use the simple interest formula for total amount A = P(1 + r · t). A = R15000(1 + 0.06 × 2) A = R15000(1 + 0.12) A = R15000(1.12) A = R16800 The amount available in his account after 2 years will be R16800. 2.3 Step 1: Calculate the amount with compound interest at 5% compounded annually for 2 years. Principal (P) = R15 000 Annual compound interest rate (i) = 5% = 0.05 Number of compounding periods (n) = 2 years Use the compound interest formula A = P(1 + i)^n. A = R15000(1 + 0.05)^2 A = R15000(1.05)^2 A = R15000(1.1025) A = R16537.50 Step 2: Compare this amount to the amount calculated in 2.2 (simple interest at 6% for 2 years). Amount with simple interest (6%) = R16 800 Amount with compound interest (5%) = R16 537.50 Step 3: Justify or refute the manager's claim. Since R16 800 > R16 537.50, Thabo would have less money with the 5% compound interest deal. Therefore, the manager's claim is refuted. Thabo's current deal of 6% simple interest is better. Question 3 Pinkie wants to invest R12 000 at an interest rate of 5% per annum for 3 years. 3.1 Step 1: Identify the principal amount, annual simple interest rate, and time. Principal (P) = R12 000 Annual simple interest rate (r) = 5% = 0.05 Time (t) = 3 years Step 2: Use the simple interest formula for total amount A = P(1 + r · t). A = R12000(1 + 0.05 × 3) A = R12000(1 + 0.15) A = R12000(1.15) A = R13800 If simple interest is added, Pinkie will have R13800 in her account. 3.2 Step 1: Identify the principal amount, annual compound interest rate, and number of compounding periods. Principal (P) = R12 000 Annual compound interest rate (i) = 5% = 0.05 Number of compounding periods (n) = 3 years (compounded annually) Step 2: Use the compound interest formula A = P(1 + i)^n. A = R12000(1 + 0.05)^3 A = R12000(1.05)^3 A = R12000(1.157625) A = R13891.50 If interest is compounded annually, Pinkie will have R13891.50 in her account. 3 done, 2 left today. You're making progress.