Question

Given a percent of decrease and an initial amount, explain how to find the final amount after the decrease. Approximately \(27 \%\) of Sheila's gross monthly income is deducted for Social Security, federal withholdings, state withholdings, and insurance. If her gross monthly salary is \(\$ 2708.33,\) what is her net pay?

Short answer

Answer: \$1977.08

Step-by-step solution

Convert the percentage to a decimal

In order to use the percentage in calculations, we need to convert it to a decimal by dividing by 100. In this case, we have \(27\%\). Divide by 100 to convert it: $$\frac{27}{100} = 0.27$$ So, the decimal equivalent of \(27 \%\) is \(0.27.\)

Calculate the amount deducted

Now, multiply the decimal equivalent of the percentage by the gross monthly salary to find the amount of deductions: $$\$2708.33 \times 0.27 = \$731.25$$ So, the total amount deducted from her gross monthly salary is \$731.25.

Find the net pay

Finally, subtract the amount deducted from the gross monthly salary to find the net pay: $$\$2708.33 - \$731.25 = \$1977.08$$ Therefore, Sheila's net pay after deductions is \$1977.08.

Key concepts

Percent of Decrease

Understanding the mindset behind 'percent of decrease' is quintessential before diving into complicated financial problems. This term refers to the reduction percent from the original amount. It is represented by a percentage that indicates how much a quantity has diminished relative to its starting value.

For instance, if an item that originally cost \(100 is now sold for \)80, it has experienced a 20% decrease in price. To find this value, you need to calculate the difference between the original and final amounts (100 - 80 = \(20\text), then divide that by the original amount (\)20 / $100 = 0.20\text), and finally, convert it to a percentage by multiplying by 100 (0.20 * 100 = 20\text%). This kind of calculation is crucial for budgeting, expense tracking, and financial analysis.

Converting Percentages to Decimals

Moving from percentages to decimals is an important skill in both mathematics and real-life scenarios, such as financial calculations and data analysis. The conversion hinges on the fact that 'percent' means 'per hundred'.

Thus, you can convert a percentage to a decimal simply by dividing it by 100. For example, to convert 27% to a decimal, divide 27 by 100, which equals 0.27. This step is vital because it aligns the percentage with the base-10 system our other numerical computations are based on, making it possible to perform arithmetic operations like multiplication and addition directly with other numeric values.

Gross to Net Salary Calculations

When budgeting or planning personal finances, discerning between gross and net salary figures is fundamental. The gross salary is the amount earned before any deductions are applied, such as taxes, social security, insurance, and retirement contributions. The net salary, on the other hand, is what an individual actually takes home after these deductions.

To determine net salary, you start with the gross amount, calculate the total deductions by converting any percentage-based deductions to a decimal form, and then multiply the gross salary by this decimal. Finally, you subtract the deduction amount from the gross salary to find the net pay. Remembering this process is instrumental in financial planning and understanding payroll and taxation documents.