Let's break down the given benefits and calculate the benefit rate step-by-step.
### Step 1: Calculate the daily salary
Ian earns [tex]$62,000 annually. To find the daily salary, we assume there are 260 working days in a year (52 weeks * 5 days per week).
\[ \text{Daily Salary} = \frac{62,000}{260} \]
\[ \text{Daily Salary} \approx 238.46 \]
### Step 2: Calculate the value of Paid Time Off (PTO)
Ian receives 15 days of PTO per year. The value of PTO can be calculated by multiplying the daily salary by the number of PTO days.
\[ \text{PTO Value} = 238.46 \times 15 \]
\[ \text{PTO Value} \approx 3,576.92 \]
### Step 3: Calculate the value of Retirement Matching
Ian's company matches 6% of his salary for retirement. The value of the retirement matching can be calculated by multiplying the annual salary by 6%.
\[ \text{Retirement Matching Value} = 62,000 \times 0.06 \]
\[ \text{Retirement Matching Value} = 3,720.00 \]
### Step 4: Calculate the value of Health Insurance
Ian's health insurance totals $[/tex]10,000, and his employer subsidizes 70% of that amount. The value of employer-subsidized health insurance can be calculated as follows:
[tex]\[ \text{Health Insurance Value} = 10,000 \times 0.70 \][/tex]
[tex]\[ \text{Health Insurance Value} = 7,000.00 \][/tex]
### Step 5: Calculate the value of FICA
FICA (Federal Insurance Contributions Act) tax rate is 7.65%. To find the FICA value, we multiply the annual salary by 7.65%.
[tex]\[ \text{FICA Value} = 62,000 \times 0.0765 \][/tex]
[tex]\[ \text{FICA Value} \approx 4,743.00 \][/tex]
### Step 6: Calculate the total benefit value
Now, we sum up all the calculated benefit values:
[tex]\[ \text{Total Benefit Value} = \text{PTO Value} + \text{Retirement Matching Value} + \text{Health Insurance Value} + \text{FICA Value} \][/tex]
[tex]\[ \text{Total Benefit Value} \approx 3,576.92 + 3,720.00 + 7,000.00 + 4,743.00 \][/tex]
[tex]\[ \text{Total Benefit Value} \approx 19,039.92 \][/tex]
### Step 7: Calculate the benefit rate as a percentage of the annual salary
Finally, we calculate the benefit rate by dividing the total benefit value by the annual salary and converting it to a percentage:
[tex]\[ \text{Benefit Rate Percent} = \left( \frac{19,039.92}{62,000} \right) \times 100 \][/tex]
[tex]\[ \text{Benefit Rate Percent} \approx 30.71\% \][/tex]
Therefore, Ian's benefit rate is approximately [tex]\( 30.71\% \)[/tex].
