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 find the depreciation rate using the reducing balance method, we use the formula: S = P(1 - r)^n where S is the selling price, P is the original purchase price, r is the depreciation rate, and n is the number of years. Step 1: Identify the given values. The original purchase price P = R250\,000. The selling price after 4 years S = R100\,000. The number of years n = 4. Step 2: Substitute the values into the formula. R100\,000 = R250\,000(1 - r)^4 Step 3: Isolate the term (1 - r)^4. (100\,000)/(250\,000) = (1 - r)^4 0.4 = (1 - r)^4 Step 4: Solve for (1 - r) by taking the fourth root of both sides. 1 - r = (0.4)^(1)/(4) 1 - r ≈ 0.7952719 Step 5: Solve for r. r = 1 - 0.7952719 r ≈ 0.2047281 Step 6: Convert the rate to a percentage. r ≈ 0.2047281 × 100\% r ≈ 20.47\% The depreciation rate is 20.47\%. Send me the next one 📸