To determine the benefit rate for Henry, we need to calculate the total value of his benefits and then express that value as a percentage of his annual salary. Here's the step-by-step solution:
1. Calculate the value of the employer-subsidized health insurance:
Henry receives a 70% subsidy on a health insurance cost of [tex]$10,000.
\[
\text{Health Insurance Subsidy} = 10000 \times \frac{70}{100} = 7000
\]
2. Calculate the value of the retirement matching:
Henry receives an 8% matching on his annual salary of $[/tex]68,000.
[tex]\[
\text{Retirement Matching} = 68000 \times \frac{8}{100} = 5440
\][/tex]
3. Calculate the FICA contribution:
FICA is calculated at 7.65% of Henry's annual salary.
[tex]\[
\text{FICA Contribution} = 68000 \times \frac{7.65}{100} = 5202
\][/tex]
4. Calculate the value of the Paid Time Off (PTO):
Assuming there are 260 workdays in a year (5 days per week for 52 weeks), calculate the value of the 15 days of PTO.
[tex]\[
\text{Daily Salary} = \frac{68000}{260}
\][/tex]
[tex]\[
\text{PTO Value} = \text{Daily Salary} \times 15 = \left(\frac{68000}{260}\right) \times 15 = 3923.08
\][/tex]
5. Calculate the total benefits:
Sum the values of all the benefits.
[tex]\[
\text{Total Benefits} = 7000 + 5440 + 5202 + 3923.08 = 21565.08
\][/tex]
6. Calculate the benefit rate as a percentage of the salary:
[tex]\[
\text{Benefit Rate} = \left(\frac{21565.08}{68000}\right) \times 100 = 31.71\%
\][/tex]
7. Round to the nearest percentage point:
The benefit rate percentage can be rounded to the nearest whole number.
[tex]\[
\text{Rounded Benefit Rate} = 32\%
\][/tex]
Therefore, the benefit rate for Henry is [tex]\( \boxed{32\%} \)[/tex].
