To calculate the benefit rate for Ian, we need to determine the total value of his benefits and then find what percentage of his salary these benefits represent. Let's break this down step by step.
1. Retirement Matching Benefit:
Ian’s salary is [tex]$62,000, and the retirement matching rate is 6%. Therefore, the retirement benefit can be calculated as:
\[
\text{Retirement Benefit} = 62000 \times 0.06 = 3720 \text{ dollars}
\]
2. Paid Time Off (PTO) Value:
Ian receives 15 days of paid time off. Assuming there are 252 working days in a year, the value of the PTO is calculated by determining the daily salary rate and then multiplying by the number of PTO days:
\[
\text{Daily Salary Rate} = \frac{62000}{252} \approx 246.03 \text{ dollars per day}
\]
\[
\text{PTO Value} = 246.03 \times 15 \approx 3690.48 \text{ dollars}
\]
3. Health Insurance Benefit:
The health insurance cost is $[/tex]10,000 annually, and Ian’s employer covers 70% of this cost. Therefore, the health insurance benefit is calculated as:
[tex]\[
\text{Health Insurance Benefit} = 10000 \times 0.70 = 7000 \text{ dollars}
\][/tex]
4. FICA Contribution:
The FICA rate is 7.65%. Thus, the FICA contribution from Ian’s salary is:
[tex]\[
\text{FICA Contribution} = 62000 \times 0.0765 = 4743 \text{ dollars}
\][/tex]
5. Total Benefits:
Adding up all these benefits gives us the total benefits Ian receives:
[tex]\[
\text{Total Benefits} = 3720 + 3690.48 + 7000 + 4743 \approx 19153.48 \text{ dollars}
\][/tex]
6. Benefit Rate:
Finally, we calculate the benefit rate as a percentage of Ian's salary:
[tex]\[
\text{Benefit Rate} = \left( \frac{19153.48}{62000} \right) \times 100 \approx 30.89 \%
\][/tex]
7. Rounding:
When we round this to the nearest percentage point, we find:
[tex]\[
\text{Rounded Benefit Rate} = 31\%
\][/tex]
So, the benefit rate for Ian is [tex]\( \boxed{31\%} \)[/tex].
