Question

if a 6.2% social security tax is applied to a maximum wage of $106,800, the maximum amount of social securit that could ever be charged in a single year is:
a. $213.60
b. $6,408.00
c. $6,621.60
d. $17,225.81

please select the best answer from the choices provided

a
b
c
d

Explanation:

Step1: Convert percentage to decimal

To calculate the tax, we first convert the percentage \( 6.2\% \) to a decimal. We do this by dividing by 100, so \( 6.2\% = \frac{6.2}{100}= 0.062 \).

Step2: Calculate the tax amount

The tax amount is calculated by multiplying the maximum wage by the tax rate. The maximum wage is \( \$106,800 \) and the tax rate is \( 0.062 \). So the tax amount \( T=106800\times0.062 \).
Calculating \( 106800\times0.062 \):

$$
LATEXBLOCK0
$$

Wait, there is a mistake in the above calculation. Wait, no, wait \( 106800\times0.062 \): Let's recalculate \( 106800\times0.062 \). \( 106800\times0.06 = 6408 \) and \( 106800\times0.002=213.6 \), then \( 6408 + 213.6=6621.6 \). But wait, the option b is \( 6408 \), option c is \( 6621.6 \). Wait, but maybe I made a mistake. Wait, the Social Security tax is applied on the wage up to the maximum wage base. Wait, maybe the question is that the 6.2% is the rate, so the tax is \( 106800\times0.062 \). Let's compute \( 106800\times0.062 \):

\( 106800\times0.062 = 106800\times\frac{62}{1000}=\frac{106800\times62}{1000} \)

\( 106800\times62 = 106800\times(60 + 2)=106800\times60+106800\times2 = 6408000+213600 = 6621600 \)

Then divide by 1000: \( \frac{6621600}{1000}=6621.6 \). So the tax amount is \( \$6621.60 \), which is option c. Wait, but maybe the question has a typo or maybe I misread. Wait, no, let's check again. Wait, the problem says "a 6.2% Social Security tax is applied to a maximum wage of $106,800". So tax = wage * tax rate = LXI2, so the answer is c. But wait, maybe the original problem has a mistake? Wait, no, let's check the options. Option c is $6,621.60, which matches our calculation.

Wait, but I think I made a mistake earlier. Wait, no, let's do the multiplication again: \( 106800\times0.062 \). Let's compute \( 106800\times0.062 \):

\( 106800\times0.062 = 106800\times\frac{62}{1000} = \frac{106800\times62}{1000} \)

\( 106800\times62 \):

\( 106800\times60 = 6408000 \)

\( 106800\times2 = 213600 \)

Sum: \( 6408000+213600 = 6621600 \)

Divide by 1000: \( 6621600\div1000 = 6621.6 \). So the tax amount is $6621.60, which is option c.

Answer:

c. $6,621.60