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Hannah earns [tex]\$52,000[/tex] per year, receives 10 days PTO, 6\% retirement matching, and receives 60\% employer-subsidized health insurance which totals [tex]\$10,000[/tex]. Calculate the benefit rate.

\begin{tabular}{|l|c|}
\hline
\multicolumn{2}{|c|}{Employee Benefits} \\
\hline
Health Insurance & 60\% \\
\hline
FICA & 7.65\% \\
\hline
Paid Vacation (PTO) & 10 days \\
\hline
Retirement Matching & 6\% \\
\hline
\end{tabular}

Round to the nearest percentage point.

Sagot :

GinnyAnsweridn
To solve this problem, we'll break it down into several steps to calculate each component of the benefits and then determine the overall benefit rate. Here's how you can approach it:

### Step 1: Calculate the Cost of Paid Vacation (PTO)
Hannah receives 10 days of paid time off (PTO) per year. To find out the value of these PTO days:

1. Calculate the daily salary:
- Annual Salary: \[tex]$52,000 - Working days in a year: 260 \[\text{Daily Salary} = \frac{\text{Annual Salary}}{\text{Working Days}} = \frac{52000}{260} = 200 \text{ dollars/day}\] 2. Calculate the value of 10 PTO days: - \[\text{PTO Value} = \text{Daily Salary} \times \text{PTO Days} = 200 \times 10 = 2000 \text{ dollars}\] ### Step 2: Calculate the Retirement Matching Contribution Hannah’s employer matches 6% of her annual salary for retirement. \[\text{Retirement Matching Value} = \text{Annual Salary} \times \text{Retirement Matching Percentage} = 52000 \times 0.06 = 3120 \text{ dollars}\] ### Step 3: Calculate the Employer's Contribution to Health Insurance The employer covers 60% of Hannah’s health insurance, which totals \$[/tex]10,000 annually.

[tex]\[\text{Health Insurance Covered Value} = \text{Total Health Insurance} \times \text{Covered Percentage} = 10000 \times 0.60 = 6000 \text{ dollars}\][/tex]

### Step 4: Calculate the FICA Contribution by the Employer
The employer's share of FICA taxes is 7.65% of Hannah’s annual salary.

[tex]\[\text{FICA Value} = \text{Annual Salary} \times \text{FICA Percentage} = 52000 \times 0.0765 = 3978 \text{ dollars}\][/tex]

### Step 5: Calculate Total Benefits
Add all the individual components of the benefits to calculate the total benefits.

[tex]\[\text{Total Benefits} = \text{PTO Value} + \text{Retirement Matching Value} + \text{Health Insurance Covered Value} + \text{FICA Value}\][/tex]
[tex]\[= 2000 + 3120 + 6000 + 3978 = 15098 \text{ dollars}\][/tex]

### Step 6: Calculate the Benefit Rate
The benefit rate is the total benefits expressed as a percentage of the annual salary.

[tex]\[\text{Benefit Rate} = \left( \frac{\text{Total Benefits}}{\text{Annual Salary}} \right) \times 100\][/tex]
[tex]\[= \left( \frac{15098}{52000} \right) \times 100 \approx 29\][/tex]

### Conclusion
The benefit rate is approximately 29%, rounded to the nearest percentage point.
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