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.
ScanSolve AI Answer
To calculate the future value of Bonita's investment for each compounding period, we use the compound interest formula: A = P(1 + (r)/(n))^nt Where: A = future value of the investment P = principal amount (R26 000) r = annual interest rate (12% or 0.12) n = number of times interest is compounded per year t = number of years Since the time period is not specified, we will assume t = 1 year for all calculations. Step 1: Calculate the future value for Annually compounded interest. For annually compounding, n = 1. A = 26000(1 + (0.12)/(1))^1 × 1 A = 26000(1 + 0.12)^1 A = 26000(1.12) A = R29120.00 Step 2: Calculate the future value for Monthly compounded interest. For monthly compounding, n = 12. A = 26000(1 + (0.12)/(12))^12 × 1 A = 26000(1 + 0.01)^12 A = 26000(1.01)^12 A ≈ 26000 × 1.12682503 A ≈ R29300.05 Step 3: Calculate the future value for Half-yearly compounded interest. For half-yearly compounding, n = 2. A = 26000(1 + (0.12)/(2))^2 × 1 A = 26000(1 + 0.06)^2 A = 26000(1.06)^2 A = 26000(1.1236) A = R29213.60 Step 4: Calculate the future value for Quarterly compounded interest. For quarterly compounding, n = 4. A = 26000(1 + (0.12)/(4))^4 × 1 A = 26000(1 + 0.03)^4 A = 26000(1.03)^4 A ≈ 26000 × 1.12550881 A ≈ R29263.23 The future values after 1 year for each compounding period are: 1. Annually: R29120.00 2. Monthly: R29300.05 3. Half-yearly: R29213.60 4. Quarterly: R29263.23 Send me the next one 📸