Question

there is a sale on computers at your local comp2u. the gaming system that you are interested in has the latest intel quad core processor and duel nvidia geforce 9800s graphics card. the sale price on the computer is $1,500.00 plus 5.1% sales tax. your monthly gross salary is $2,500. how much will you have saved over a two month period and will you be able to afford the computer, given your monthly expenses total $1,250, social security is 6.2% of your biweekly income, medicare is 1.45% of your biweekly income, and you pay state and federal taxes in the amount of $45.00 and $89.51 biweekly respectively? a. $1,576.5; yes b. $1,521.2; no c. $1,579.44; yes d. $1,561.32; no please select the best answer from the choices provided

Explanation:

Step1: Calculate the cost of the computer

The sale price of the computer is \( \$1500\). The sales tax is \(5.1\%\) of \(1500\).
The sales - tax amount is \(1500\times0.051=\$76.5\).
The total cost of the computer is \(1500 + 76.5=\$1576.5\).

Step2: Calculate the bi - weekly income

The monthly gross salary is \( \$2500\), so the bi - weekly income \(I=\frac{2500}{2}=\$1250\).

Step3: Calculate the deductions per bi - week

Social Security deduction: \(0.062\times1250=\$77.5\)
Medicare deduction: \(0.0145\times1250=\$18.125\)
State tax: \( \$45\)
Federal tax: \( \$89.51\)
Total deductions per bi - week \(D = 77.5+18.125 + 45+89.51=\$229.135\)

Step4: Calculate the savings per month

Net income per bi - week \(=1250 - 229.135=\$1020.865\)
Net income per month \(=1020.865\times2=\$2041.73\)
Monthly expenses \(E=\$1250\)
Savings per month \(S=2041.73 - 1250=\$791.73\)

Step5: Calculate the savings over two months

Savings over two months \(=791.73\times2=\$1583.46\) (approximate value, due to rounding differences in bi - weekly calculations, if we calculate more precisely:
Net income per bi - week:
\(1250-(1250\times0.062 + 1250\times0.0145+45 + 89.51)=1250-(77.5+18.125 + 45+89.51)=1250 - 229.135 = 1020.865\)
Two - month (4 bi - weeks) net income \(=1020.865\times4=\$4083.46\)
Two - month expenses \(=1250\times2=\$2500\)
Two - month savings \(=4083.46-2500=\$1583.46\). But if we calculate using the formula:
Let's recast.
Monthly net income \(y\):
\(y=(2500-(2500\times0.062 + 2500\times0.0145+45\times2+89.51\times2))-1250\)
\(y=(2500-(155 + 36.25+90 + 179.02))-1250\)
\(y=(2500 - 460.27)-1250\)
\(y = 2039.73-1250=\$789.73\)
Two - month savings \(=789.73\times2=\$1579.46\approx\$1579.44\) (due to rounding in tax calculations at the bi - weekly level)

Answer:

C. \(\$1,579.44\); yes