Source:MPUM P2 Pre The above TABLE 1 to answer the following questions. Show how the value of R59 314 in tax bracket 3 was calculated. During August 2014 Miss Gumede's monthly salary of R29 915 was incroased by \( 7.5 \% \), and she had to pay a monthly tax amount of 6667,90 . Verly 0 calculation if the tax amount is correct.

To solve the problem, we need to follow these steps: 1. **Calculate Miss Gumede's new salary after the increase.** 2. **Determine the tax amount based on the new salary and the tax bracket.** 3. **Verify if the tax amount of R6,667.90 is correct.** ### Step 1: Calculate the New Salary Miss Gumede's original salary is R29,915, and it was increased by 7.5%. To calculate the new salary, we can use the formula: \[ \text{New Salary} = \text{Original Salary} + \left( \text{Original Salary} \times \frac{\text{Percentage Increase}}{100} \right) \] Substituting the values: \[ \text{New Salary} = 29915 + \left( 29915 \times \frac{7.5}{100} \right) \] Now, let's calculate this value. ### Step 2: Calculate the Tax Amount Based on the New Salary Next, we need to determine the tax amount based on the new salary. However, we need to know the tax brackets to calculate the tax amount correctly. Since the problem refers to "tax bracket 3" and a specific value of R59,314, we will assume that this is the threshold for tax bracket 3. ### Step 3: Verify the Tax Amount To verify if the tax amount of R6,667.90 is correct, we will need to calculate the tax based on the new salary and the tax brackets. Let's perform the calculations for the new salary first. I'll calculate the new salary now. Calculate the value by following steps: - step0: Calculate: \(29915+\left(\frac{29915\times 7.5}{100}\right)\) - step1: Multiply the numbers: \(29915+\left(\frac{224362.5}{100}\right)\) - step2: Divide the terms: \(29915+\frac{17949}{8}\) - step3: Reduce fractions to a common denominator: \(\frac{29915\times 8}{8}+\frac{17949}{8}\) - step4: Transform the expression: \(\frac{29915\times 8+17949}{8}\) - step5: Multiply the numbers: \(\frac{239320+17949}{8}\) - step6: Add the numbers: \(\frac{257269}{8}\) The new salary after the 7.5% increase is approximately R32,158.63. ### Step 1: New Salary Calculation - **Original Salary:** R29,915 - **Increase:** \( 7.5\% \) of R29,915 = R2,243.63 (approximately) - **New Salary:** R29,915 + R2,243.63 = R32,158.63 ### Step 2: Determine the Tax Amount Now, we need to determine the tax amount based on the new salary of R32,158.63. Since we don't have the specific tax brackets, we will assume that the tax amount of R6,667.90 is based on the new salary and the tax bracket system. ### Step 3: Verify the Tax Amount To verify if R6,667.90 is correct, we need to check if this amount aligns with the tax bracket for a salary of R32,158.63. Assuming that R59,314 is the threshold for tax bracket 3, we can infer that Miss Gumede's salary falls below this threshold. Therefore, we need to check the tax rate applicable to her salary. Since we don't have the exact tax rates, we can only verify if the tax amount seems reasonable based on the new salary. Let's calculate the effective tax rate that would result in a tax amount of R6,667.90 from the new salary of R32,158.63: \[ \text{Effective Tax Rate} = \frac{\text{Tax Amount}}{\text{New Salary}} \times 100 \] Substituting the values: \[ \text{Effective Tax Rate} = \frac{6667.90}{32158.63} \times 100 \] Now, let's calculate the effective tax rate. Calculate the value by following steps: - step0: Calculate: \(\left(\frac{6667.9}{32158.63}\right)\times 100\) - step1: Divide the terms: \(\frac{666790}{3215863}\times 100\) - step2: Multiply: \(\frac{666790\times 100}{3215863}\) - step3: Multiply: \(\frac{66679000}{3215863}\) The effective tax rate calculated from the tax amount of R6,667.90 and the new salary of R32,158.63 is approximately \( 20.73\% \). ### Summary of Calculations 1. **New Salary Calculation:** - Original Salary: R29,915 - Increase: R2,243.63 (7.5%) - New Salary: R32,158.63 2. **Effective Tax Rate Calculation:** - Tax Amount: R6,667.90 - Effective Tax Rate: \( \approx 20.73\% \) ### Conclusion The tax amount of R6,667.90 corresponds to an effective tax rate of approximately 20.73% based on Miss Gumede's new salary of R32,158.63. If this rate aligns with the tax bracket system, then the tax amount is correct. If the tax brackets indicate a different rate for her salary, then further investigation would be needed to confirm the accuracy of the tax amount.