Problem 67 - College Algebra and Calculus: An Applied Approach

Question

Projected Expenses From January through May, a company's expenses totaled \(\$ 325,450\). If the monthly expenses continue at this rate, what will be the total expenses for the year?

Step-by-Step Solution

Answer

If the company continues to spend at the same rate as it did from January to May, its projected total expenses for the year would be calculated as follows: Step 1: \( \frac{325,450}{5} = \$65,090 \) which is the average monthly expense. Step 2: \( 65,090 \times 12 = \$781,080 \). Thus, the projected total expenses for the year will be \$781,080.

Step 1: Calculate average monthly expenses

We are given that for the initial five months, the company spent $325,450. We can determine the average monthly expenses by dividing $325,450 by 5. This would give us the total amount the company spends, on average, per month.

Step 2: Estimate yearly expenses

Next, we multiply the average monthly expense obtained in step 1 by 12, as there are 12 months in a year. This will give the projected total cost for the whole year, provided the company continues at this same rate.

Key Concepts

Expense Projection

Expense projection is a vital tool for businesses to plan their finances and allocate resources effectively. It involves estimating future costs based on current or historical data. In the context of the exercise, the company had expenses totaling $325,450 over the first five months. By projecting expenses, businesses can anticipate future spending patterns. This helps in:

• Identifying potential cash flow issues.
• Planning budgets more effectively.
• Making informed strategic decisions.

By maintaining consistency in expense patterns, businesses use expense projection to allocate sufficient funds for future financial commitments. This is particularly useful for long-term strategic planning and management of resources.

Average Calculation

Average calculation is a basic arithmetic operation that helps us find the central value of a set of numbers. For the exercise, to find the monthly average expense, we divide the total expenses incurred over five months, $325,450, by the number of months, which is 5. This calculation is well-represented as:\[\text{Average monthly expenses} = \frac{325,450}{5}\]By performing this division, we can obtain a figure that represents what the company spends each month, on average.
This step is essential because it gives a baseline for projecting future expenses. Knowing the average allows businesses to understand their spending habits and predict future expenses accurately.

Yearly Estimation

Yearly estimation is an extension of average calculation and aims to provide a comprehensive view of potential expenses over a longer period. Once we have determined the average monthly expenses, multiplying this figure by 12 gives the estimated expenses for the entire year. Mathematically, it can be expressed as:\[\text{Yearly expenses} = \text{Average monthly expenses} \times 12\]Using this calculation, businesses ensure they have a broader view of their fiscal commitments. Yearly estimation is crucial for:

• Setting annual budgets.
• Determining long-term financial strategies.
• Ensuring sufficient funding is in place for expected expenses.

In conclusion, yearly estimation is a fundamental part of financial planning and helps smooth out any unexpected expenses by providing a clearer picture of the year ahead.