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 determine the amount Makgabo still needs, we first need to calculate the future value of her savings. This is an annuity problem. Here are the given details: Total amount needed = R45,000 Monthly deposit (Pmt) = R2,200 Number of months (n) = 16 Annual interest rate = 15.4% Interest compounded monthly, so the monthly interest rate (i) = (0.154)/(12) Since Makgabo "starts to save immediately" by depositing R2,200 every month, this is an annuity due. The future value of an annuity due (FV_due) is given by the formula: FV_due = Pmt · s_n|i · (1+i) where s_n|i = ((1+i)^n - 1)/(i) is the future value interest factor of an ordinary annuity. Step 1: Calculate the future value of Makgabo's savings. Substitute the given values into the annuity due formula: FV_savings = 2200 · s_16|(0.154)/(12) · (1 + (0.154)/(12)) Step 2: Calculate the amount Makgabo still needs. The amount she still needs (X) is the total amount required minus the future value of her savings: X = Total amount needed - FV_savings X = 45000 - [2200 · s_16|(0.154)/(12) · (1 + (0.154)/(12))] Comparing this expression with the given options, we can see that option d matches our derived formula, where i in (1+i) represents the monthly interest rate (0.154)/(12). The correct option is d. X = 45000 - (1 + i)2200s_16|0.154/12 where i = (0.154)/(12). That's 2 down. 3 left today — send the next one.