Problem 61 - Algebra and Trigonometry

Question

Depreciation The purchase value of an office computer is \(\$ 12,500 .\) Its annual depreciation is \(\$ 1875 .\) Find the value of the computer after 6 years.

Step-by-Step Solution

Answer

The computer's value after 6 years is \(\$1250\).

Step 1: Understand the Problem

We need to find the value of the computer after 6 years, given its initial purchase value and annual depreciation amount.

Step 2: Identify Initial Value and Depreciation

The initial purchase value of the computer is \(\\(12,500\) and the annual depreciation amount is \(\\)1875\).

Step 3: Calculate Total Depreciation Over 6 Years

To find the total depreciation over 6 years, multiply the annual depreciation by 6: \( 6 \times 1875 = 11250 \).

Step 4: Subtract Total Depreciation From Initial Value

Subtract the total depreciation from the initial purchase value to find the value after 6 years: \( 12500 - 11250 = 1250 \).

Step 5: Conclusion

The value of the computer after 6 years is \(\$1250\).

Key Concepts

Office Computer Valuation

Determining the current value of your office equipment, like a computer, can be crucial for financial planning and accounting purposes. Office computer valuation involves understanding how much a piece of equipment is worth at any given point in time. When a computer is first purchased, it's listed at its purchase price. Over time, factors such as technological advances or wear and tear reduce its market value. This process of reduction is known as depreciation.
Depreciation gives you a realistic idea of what your computer could be worth if you decide to sell it, or how much value it has lost over a period.
Knowing the depreciated value of your office computer helps

• allocate your budget more efficiently,
• decide when to replace it, and
• support inventory management with updated assessments of total assets.

Annual Depreciation

Annual depreciation refers to how much value an asset loses over the course of a year. It is often used to allocate the cost of a tangible asset over its useful life. By understanding and calculating annual depreciation, businesses can manage their tax liabilities and financial statements more accurately.
In the case of the office computer mentioned, annual depreciation is calculated as a fixed amount of \(\$1875\). This figure is subtracted from the asset’s value each year. This process helps with forecasting value over time, assisting in preparing for future expenditures.
Here is how you calculate annual depreciation:

• Start with the initial purchase value of the asset.
• Determine the annual depreciation amount, based on historical data or assessments.
• Subtract this amount each year to find the asset’s decreasing value.

Calculating annual depreciation helps maintain a realistic view of an asset's decreasing value and aids in effective decision-making regarding equipment replacement or upgrades.

Mathematical Problem Solving

Mathematical problem solving is a critical skill, especially in business and finance. It involves breaking down complex problems into smaller, manageable steps and applying mathematical concepts to find solutions.
In the scenario of calculating a computer's depreciated value after 6 years, problem solving was essential:

• First, identify the initial problem and the data given, like the starting value and depreciation rate.
• Establish the method of computation, such as multiplying the annual depreciation by the number of years.
• Calculate the total depreciation over the period, \(6 \times 1875\), which equals \(\\(11250\).
• Finally, subtract this from the initial value to find the remaining value, which is \(\\)1250\) after 6 years.

Developing strong mathematical problem-solving skills equips you to handle various practical issues effectively, leading to informed decision-making and better management of financial resources.