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Answer :
Sure! Let's break down the process of calculating the benefit rate step-by-step, using Sofia's salary and benefits information.
1. Calculate Health Insurance Benefit:
- Sofia's employer subsidizes 70% of her health insurance, which totals [tex]$10,000.
- Therefore, the health insurance benefit from her employer is 70% of $[/tex]10,000.
- Calculation: [tex]\( 10,000 \times 0.70 = 7,000 \)[/tex]
2. Calculate the Paid Time Off (PTO) Benefit:
- Sofia receives 15 days of paid time off.
- Assuming there are 260 working days in a year, we need to find the value of this PTO.
- Calculation: [tex]\( \left(\frac{15}{260}\right) \times 70,000 = 4,038.46 \)[/tex]
3. Calculate Retirement Matching Benefit:
- The retirement matching is 8% of Sofia's salary.
- Calculation: [tex]\( 70,000 \times 0.08 = 5,600 \)[/tex]
4. Calculate FICA Contribution:
- FICA is a standard employment contribution, here at a rate of 7.65% of the salary.
- Calculation: [tex]\( 70,000 \times 0.0765 = 5,355 \)[/tex]
5. Total Benefit Value:
- Add up all the benefits calculated: health insurance, PTO, retirement matching, and FICA contribution.
- Calculation: [tex]\( 7,000 + 4,038.46 + 5,600 + 5,355 = 21,993.46 \)[/tex]
6. Calculate Benefit Rate:
- The benefit rate is the total benefit value as a percentage of Sofia's annual salary.
- Calculation: [tex]\( \frac{21,993.46}{70,000} \times 100 \approx 31.42 \% \)[/tex]
7. Round to the Nearest Percentage:
- Round [tex]\( 31.42\% \)[/tex] to the nearest whole number, which is 31%.
Therefore, Sofia's benefit rate, rounded to the nearest percentage, is 31%.
1. Calculate Health Insurance Benefit:
- Sofia's employer subsidizes 70% of her health insurance, which totals [tex]$10,000.
- Therefore, the health insurance benefit from her employer is 70% of $[/tex]10,000.
- Calculation: [tex]\( 10,000 \times 0.70 = 7,000 \)[/tex]
2. Calculate the Paid Time Off (PTO) Benefit:
- Sofia receives 15 days of paid time off.
- Assuming there are 260 working days in a year, we need to find the value of this PTO.
- Calculation: [tex]\( \left(\frac{15}{260}\right) \times 70,000 = 4,038.46 \)[/tex]
3. Calculate Retirement Matching Benefit:
- The retirement matching is 8% of Sofia's salary.
- Calculation: [tex]\( 70,000 \times 0.08 = 5,600 \)[/tex]
4. Calculate FICA Contribution:
- FICA is a standard employment contribution, here at a rate of 7.65% of the salary.
- Calculation: [tex]\( 70,000 \times 0.0765 = 5,355 \)[/tex]
5. Total Benefit Value:
- Add up all the benefits calculated: health insurance, PTO, retirement matching, and FICA contribution.
- Calculation: [tex]\( 7,000 + 4,038.46 + 5,600 + 5,355 = 21,993.46 \)[/tex]
6. Calculate Benefit Rate:
- The benefit rate is the total benefit value as a percentage of Sofia's annual salary.
- Calculation: [tex]\( \frac{21,993.46}{70,000} \times 100 \approx 31.42 \% \)[/tex]
7. Round to the Nearest Percentage:
- Round [tex]\( 31.42\% \)[/tex] to the nearest whole number, which is 31%.
Therefore, Sofia's benefit rate, rounded to the nearest percentage, is 31%.
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