To determine the benefit rate given Joe's annual earnings and benefits, we'll follow a detailed, step-by-step approach.
1. Calculate the Employer Contribution to Health Insurance:
Joe's employer covers 60% of his health insurance, and the total value of the health insurance is $10,000.
[tex]\[
\text{Health Insurance Contribution} = 0.60 \times 10{,}000 = 6{,}000
\][/tex]
2. Calculate the Employer Contribution to Retirement Matching:
Joe's employer matches 8% of his annual salary for retirement.
[tex]\[
\text{Retirement Matching Contribution} = 0.08 \times 62{,}000 = 4{,}960
\][/tex]
3. Calculate the Value of 10 Days Paid Time Off (PTO):
Joe's annual salary is $62,000, and he receives 10 days of paid time off. We'll calculate the daily rate first:
[tex]\[
\text{Daily Salary} = \frac{62{,}000}{365} \approx 169.86
\][/tex]
Then, we'll compute the value of 10 PTO days:
[tex]\[
\text{Value of 10 Days PTO} = 10 \times 169.86 = 1{,}698.63
\][/tex]
4. Calculate the Total Value of Benefits:
Add the values of the employer contributions to health insurance, retirement matching, and PTO:
[tex]\[
\text{Total Benefits} = 6{,}000 + 4{,}960 + 1{,}698.63 = 12{,}658.63
\][/tex]
5. Calculate the Benefit Rate:
Finally, we'll calculate the benefit rate by expressing the total value of benefits as a percentage of Joe's annual salary:
[tex]\[
\text{Benefit Rate} = \left( \frac{12{,}658.63}{62{,}000} \right) \times 100 \approx 20 \%
\][/tex]
Therefore, Joe's benefit rate is 20%.
