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
Step 1: Calculate the amount in the account after the first three years. The formula for compound interest is A = P(1 + r)^t. Given: • Principal (P) = R 6500 • Interest rate (r) = 12\% per annum = 0.12 • Time (t) = 3 years A_1 = 6500(1 + 0.12)^3 A_1 = 6500(1.12)^3 A_1 = 6500 × 1.404928 A_1 = 9132.032 Step 2: Subtract the withdrawal amount to find the new principal for the next period. Hannah withdraws R 4200. New principal (P_2) = A_1 - 4200 P_2 = 9132.032 - 4200 P_2 = 4932.032 Step 3: Calculate the amount in the account at the end of the next three years (total six years). Given: • New principal (P_2) = R 4932.032 • Interest rate (r) = 8\% per annum = 0.08 • Time (t) = 3 years A_2 = 4932.032(1 + 0.08)^3 A_2 = 4932.032(1.08)^3 A_2 = 4932.032 × 1.259712 A_2 = 6212.9409... Step 4: Round the final amount to two decimal places. The amount in the account at the end of the six years is R 6212.94. This matches option A. The final answer is A. R 6212.94. Last free one today — make it count tomorrow, or type /upgrade for unlimited.