Question

In 2008, the Social Security percentage was 6.2% for the first $102,000 earned. The Medicare percentage was 1.45% of your entire salary. Darby made $143,000 in 2008.

a. Write the combined taxes, y, as a piecewise function where x represents the income.

b. How much did Darby pay in Social Security tax?

c. How much did Darby pay in Medicare tax?

Answer 1

Let x be the income.

Let y be the combined taxes.

When
`x <102,000` then the income is less than maximum taxable income. Hence, we will pay social security tax on the whole income.

Social security tax =
`0.062* x=0.062x`

When
`x\geq 102000` then we will pay social security on the maximum taxable income.

Social security tax =
`0.062*102000=6324` dollars

Hence, Darby paid $6324 in Social Security tax.

Medicare tax will be =
`0.0145* x=0.0145x`

So, Darby paid in medicare tax =
`0.0145*143000=2073.50` dollars

Now combined tax or y = social security tax plus medicare tax

So,
`y=0.062x+0.0145x=0.0765x` when x<102000

and
`y=6324+0.0145x` when x≥102000

Answer 2

a. The combined taxes is represented by y and your total income is represented by x

Now, if the salary is greater than 102,000 social security is a fixed amount that is equal = 102,000*0.062 = 6,324. This is because you pay social security tax only on your first 102,000

The piece wise function is as follows:

y = 0.062*x +0.0145*x if x <=102,000

y = 6,324 + 0.0145*x if x>102,000

b. John's social security = 102,000*0.062 = $6,324 (Since you pay social security tax only on your first 102,000)

c. John's medicare tax = 0.0145*102,000 = $1,479