Sure, let's break down the problem step by step to calculate the benefit rate for Ian and then round it to the nearest percentage point.
### Step 1: Calculate the daily salary
First, we need to determine Ian's daily salary. Assuming Ian works 260 days a year:
[tex]\[
\text{daily salary} = \frac{\$62,000}{260} = \$238.46
\][/tex]
### Step 2: Calculate the value of Paid Time Off (PTO)
Next, we calculate the total value of the paid vacation days Ian receives. He has 15 days of PTO.
[tex]\[
\text{PTO value} = \text{daily salary} \times \text{PTO days} = \$238.46 \times 15 = \$3576.92
\][/tex]
### Step 3: Calculate the value of the retirement matching
Ian receives a 6% retirement matching:
[tex]\[
\text{Retirement matching value} = \text{annual salary} \times \text{retirement matching rate} = \$62,000 \times 0.06 = \$3720
\][/tex]
### Step 4: Calculate the value of the health insurance
The company pays 70% of the health insurance cost, which totals to [tex]$10,000.
\[
\text{Health insurance value} = \text{health insurance cost} \times \text{health insurance percent} = \$[/tex]10,000 \times 0.70 = \[tex]$7000
\]
### Step 5: Calculate the total benefit value
Sum up all the benefits Ian receives:
\[
\text{Total benefit value} = \text{PTO value} + \text{Retirement matching value} + \text{Health insurance value} = \$[/tex]3576.92 + \[tex]$3720 + \$[/tex]7000 = \$14296.92
\]
### Step 6: Calculate the benefit rate
The benefit rate is the total benefit value divided by the annual salary, expressed as a percentage:
[tex]\[
\text{Benefit rate} = \left(\frac{\text{Total benefit value}}{\text{annual salary}} \right) \times 100 = \left(\frac{14296.92}{62000} \right) \times 100 \approx 23.06\%
\][/tex]
### Step 7: Round to the nearest percentage point
Finally, we round the benefit rate to the nearest percentage point:
[tex]\[
\text{Benefit rate (rounded)} = 23\%
\][/tex]
So, Ian's benefit rate is 23% rounded to the nearest percentage point.
