Answer :
To calculate Rachel's benefit rate, we will consider the different components of her benefits: health insurance, FICA, PTO, and retirement matching. Here’s a step-by-step breakdown of the calculations:
1. Health Insurance:
- Rachel's employer covers 60% of a total health insurance cost of $10,000.
- Health Insurance Benefit: [tex]\(0.60 \times 10,000 = 6,000\)[/tex]
2. FICA (Federal Insurance Contributions Act):
- Rachel's FICA contribution is 7.65% of her salary.
- FICA Benefit: [tex]\(0.0765 \times 52,000 = 3,978\)[/tex]
3. Retirement Matching:
- Rachel's employer matches 8% of her salary for retirement savings.
- Retirement Matching Benefit: [tex]\(0.08 \times 52,000 = 4,160\)[/tex]
4. Paid Time Off (PTO):
- Rachel receives 15 days of paid vacation out of a typical 260 working days in a year.
- The value of her PTO is calculated based on her daily salary rate.
- Rachel's daily salary rate: [tex]\(\frac{52,000}{260} = 200\)[/tex]
- PTO Benefit: [tex]\( 15 \times 200 = 3,000\)[/tex]
5. Total Benefits:
- We add up all the individual benefits.
- Total Benefits: [tex]\(6,000 \text{ (Health Insurance)} + 3,978 \text{ (FICA)} + 4,160 \text{ (Retirement Matching)} + 3,000 \text{ (PTO)} = 17,138\)[/tex]
6. Benefit Rate Calculation:
- The benefit rate is calculated as the ratio of the total benefits to the annual salary, expressed as a percentage.
- Benefit Rate: [tex]\(\left(\frac{17,138}{52,000}\right) \times 100 \approx 32.958\%\)[/tex]
7. Rounding to the Nearest Percentage Point:
- Rounding 32.958% to the nearest percentage point: [tex]\(33\%\)[/tex]
Thus, Rachel's benefit rate is 33% when rounded to the nearest percentage point.
1. Health Insurance:
- Rachel's employer covers 60% of a total health insurance cost of $10,000.
- Health Insurance Benefit: [tex]\(0.60 \times 10,000 = 6,000\)[/tex]
2. FICA (Federal Insurance Contributions Act):
- Rachel's FICA contribution is 7.65% of her salary.
- FICA Benefit: [tex]\(0.0765 \times 52,000 = 3,978\)[/tex]
3. Retirement Matching:
- Rachel's employer matches 8% of her salary for retirement savings.
- Retirement Matching Benefit: [tex]\(0.08 \times 52,000 = 4,160\)[/tex]
4. Paid Time Off (PTO):
- Rachel receives 15 days of paid vacation out of a typical 260 working days in a year.
- The value of her PTO is calculated based on her daily salary rate.
- Rachel's daily salary rate: [tex]\(\frac{52,000}{260} = 200\)[/tex]
- PTO Benefit: [tex]\( 15 \times 200 = 3,000\)[/tex]
5. Total Benefits:
- We add up all the individual benefits.
- Total Benefits: [tex]\(6,000 \text{ (Health Insurance)} + 3,978 \text{ (FICA)} + 4,160 \text{ (Retirement Matching)} + 3,000 \text{ (PTO)} = 17,138\)[/tex]
6. Benefit Rate Calculation:
- The benefit rate is calculated as the ratio of the total benefits to the annual salary, expressed as a percentage.
- Benefit Rate: [tex]\(\left(\frac{17,138}{52,000}\right) \times 100 \approx 32.958\%\)[/tex]
7. Rounding to the Nearest Percentage Point:
- Rounding 32.958% to the nearest percentage point: [tex]\(33\%\)[/tex]
Thus, Rachel's benefit rate is 33% when rounded to the nearest percentage point.
