MATH SOLVE

3 months ago

Q:
# jennifer made $74,900 last year she pay 6% state income tax, 15% federal income tax 6.2% for social security and 1.45% for medicare what is her monthly income? what was her net monthly income

Accepted Solution

A:

The idea here is that $74,900 is Jennifer's annual salary before the deductions (the taxes, social security and medicare). Since she pays 6% in state taxes, 15% in federal taxes, 6.2% in social security and 1.45% in medicare, the deductions total 6% + 15% + 6.2% + 1.45% = 28.65%. To find out what she keeps we do the total (100%) less the deductions (28.65%) which yields 71.35%. That is, she keeps 71.35% of the total amount given ($74,900).

Recall, that percent means out of ("per") 100 ("cent" --> think "century= 100 years). So, 71.35% means 71.35 out of 100. That is [tex] \frac{71.35}{100}=.7135 [/tex]. To find 71.35% of 74,900 we multiply [tex](.7135)(74900)=53,441.15[/tex]. That means that Jennifer keeps $53,441.15 of what she makes.

We are asked for her monthly net income. That is, how much money does she take home per month after the deductions. If we assume that she is paid the same amount each month, to find her monthly net income we divide 53,441.15 by 12.

Jennifer's net monthly income is [tex] \frac{53441.15}{12}=$4,453.43 [/tex]

Note that when we divide by 12 above we actually get 4,453.42916 but as this is money I rounded to $4,453.43. In reality this is a little bit too high as 4,453.43 times 12 = 53,441.16. That means we overpaid her by one penny. In real life she probably would get 11 paychecks at $4,453.43 and one paycheck at $4,453.42 to make up for the penny, but if this is a textbook problem I expect the rounding up would be acceptable.

Recall, that percent means out of ("per") 100 ("cent" --> think "century= 100 years). So, 71.35% means 71.35 out of 100. That is [tex] \frac{71.35}{100}=.7135 [/tex]. To find 71.35% of 74,900 we multiply [tex](.7135)(74900)=53,441.15[/tex]. That means that Jennifer keeps $53,441.15 of what she makes.

We are asked for her monthly net income. That is, how much money does she take home per month after the deductions. If we assume that she is paid the same amount each month, to find her monthly net income we divide 53,441.15 by 12.

Jennifer's net monthly income is [tex] \frac{53441.15}{12}=$4,453.43 [/tex]

Note that when we divide by 12 above we actually get 4,453.42916 but as this is money I rounded to $4,453.43. In reality this is a little bit too high as 4,453.43 times 12 = 53,441.16. That means we overpaid her by one penny. In real life she probably would get 11 paychecks at $4,453.43 and one paycheck at $4,453.42 to make up for the penny, but if this is a textbook problem I expect the rounding up would be acceptable.