Answer :
To calculate Henry's benefit rate, we need to evaluate all the employee benefits he receives and then find out what percentage of his salary these benefits represent. Here's a step-by-step breakdown of the calculations:
1. Health Insurance:
Henry's employer covers 70% of the total health insurance cost, which is \[tex]$10,000. \[ \text{Employer's contribution} = 0.70 \times 10,000 = \$[/tex]7,000
\]
2. FICA Contribution:
The FICA rate is 7.65% of his salary.
[tex]\[ \text{FICA contribution} = 0.0765 \times 68,000 = \$5,202 \][/tex]
3. Paid Time Off (PTO):
Henry gets 15 days of paid time off. Assuming there are 260 working days in a year:
[tex]\[ \text{Value of PTO} = \left( \frac{68,000}{260} \right) \times 15 = \frac{68,000}{260} \cdot 15 = 261.53846153846155 \cdot 15 = \$3,923.08 \][/tex]
4. Retirement Matching:
The employer matches 8% of Henry's salary for retirement.
[tex]\[ \text{Retirement matching} = 0.08 \times 68,000 = \$5,440 \][/tex]
5. Total Benefits:
Summing up all the benefits:
[tex]\[ \text{Total Benefits} = 7,000 + 5,202 + 3,923.08 + 5,440 = \$21,565.08 \][/tex]
6. Benefit Rate:
To find the benefit rate, we calculate the percentage of the total benefits relative to his salary.
[tex]\[ \text{Benefit rate} = \left( \frac{21,565.08}{68,000} \right) \times 100 = 31.713348416289588\% \][/tex]
7. Rounded Benefit Rate:
Finally, we round this percentage to the nearest whole number:
[tex]\[ \text{Rounded benefit rate} = 32\% \][/tex]
So, the benefit rate for Henry is [tex]\( \boxed{32\%} \)[/tex].
1. Health Insurance:
Henry's employer covers 70% of the total health insurance cost, which is \[tex]$10,000. \[ \text{Employer's contribution} = 0.70 \times 10,000 = \$[/tex]7,000
\]
2. FICA Contribution:
The FICA rate is 7.65% of his salary.
[tex]\[ \text{FICA contribution} = 0.0765 \times 68,000 = \$5,202 \][/tex]
3. Paid Time Off (PTO):
Henry gets 15 days of paid time off. Assuming there are 260 working days in a year:
[tex]\[ \text{Value of PTO} = \left( \frac{68,000}{260} \right) \times 15 = \frac{68,000}{260} \cdot 15 = 261.53846153846155 \cdot 15 = \$3,923.08 \][/tex]
4. Retirement Matching:
The employer matches 8% of Henry's salary for retirement.
[tex]\[ \text{Retirement matching} = 0.08 \times 68,000 = \$5,440 \][/tex]
5. Total Benefits:
Summing up all the benefits:
[tex]\[ \text{Total Benefits} = 7,000 + 5,202 + 3,923.08 + 5,440 = \$21,565.08 \][/tex]
6. Benefit Rate:
To find the benefit rate, we calculate the percentage of the total benefits relative to his salary.
[tex]\[ \text{Benefit rate} = \left( \frac{21,565.08}{68,000} \right) \times 100 = 31.713348416289588\% \][/tex]
7. Rounded Benefit Rate:
Finally, we round this percentage to the nearest whole number:
[tex]\[ \text{Rounded benefit rate} = 32\% \][/tex]
So, the benefit rate for Henry is [tex]\( \boxed{32\%} \)[/tex].
