To calculate Henry's benefit rate step-by-step, follow these instructions:
1. Determine the value of the health insurance subsidy:
- The total cost of health insurance is \[tex]$10,000.
- Henry’s employer covers 70% of the health insurance.
\( \text{Health insurance value} = 10\,000 \times 0.70 = 7\,000 \)
2. Calculate the value of retirement matching:
- Henry's salary is \$[/tex]68,000.
- The retirement matching rate is 8%.
[tex]\( \text{Retirement matching value} = 68\,000 \times 0.08 = 5\,440 \)[/tex]
3. Calculate the value of Paid Time Off (PTO):
- Henry receives 15 days of PTO per year.
- There are 260 workdays per year (assuming a 5-day work week and 52 weeks in a year).
- First, calculate Henry’s daily salary.
[tex]\( \text{Daily salary} = \frac{68\,000}{260} \approx 261.54 \)[/tex]
- Calculate the value of 15 days of PTO.
[tex]\( \text{PTO value} = 15 \times 261.54 \approx 3\,923.08 \)[/tex]
4. Sum up all the benefits:
- Health insurance value: \[tex]$7,000
- Retirement matching value: \$[/tex]5,440
- PTO value: \$3,923.08
[tex]\( \text{Total benefits} = 7\,000 + 5\,440 + 3\,923.08 = 16\,363.08 \)[/tex]
5. Calculate the benefit rate:
- Divide total benefits by Henry's salary.
[tex]\( \text{Benefit rate} = \left( \frac{16\,363.08}{68\,000} \right) \times 100 \approx 24.06 \)[/tex]
6. Round to the nearest percentage point:
[tex]\( \text{Benefit rate (rounded)} = 24\% \)[/tex]
Thus, the benefit rate is [tex]\(24\%\)[/tex].
