Bob’s employer covers 23% of his family’s annual health insurance premium. The balance of the premium is deducted in equal amounts from Bob’s paycheck 26 times over the calendar year. If $185.30 is withheld from each of Bob’s paychecks, what is his family’s annual health insurance premium?

Question

a.
$805.65
b.
$4,817.80
c.
$6,256.88
d.
$20,946.96

Answer 1

To find Bob's family's annual health insurance premium, we need to first determine the total amount that Bob pays from his paychecks in a year.

Since Bob has 26 pay periods and $185.30 is withheld from each paycheck, we can calculate the total amount Bob pays annually:

\[ \text{Total withheld from paychecks} = \text{Amount per paycheck} \times \text{Number of paychecks} \]

\[ \text{Total withheld from paychecks} = 185.30 \times 26 = 4,817.80 \]

This amount represents 77% of the total premium (since his employer covers 23% of the premium, Bob covers the remaining 77%). Let \( P \) be the annual health insurance premium. The relationship can be expressed as:

\[ 0.77P = 4,817.80 \]

To find \( P \), we can solve for it:

\[ P = \frac{4,817.80}{0.77} \]

Calculating \( P \):

\[ P \approx 6,256.88 \]

Thus, Bob's family's annual health insurance premium is approximately:

\[ \boxed{6,256.88} \]