Problem 8 - Algebra 2

Question

Zeus Industries bought a computer for \(\$ 2500 .\) If it depreciates at a rate of 20\(\%\) per year, what will be its value in 2 years?

Step-by-Step Solution

Answer

The computer's value will be $1600 after two years.

Step 1: Understanding Depreciation

To solve this problem, we first need to understand that depreciation is the reduction in the value of an asset over time. Here, the computer's value depreciates at a rate of 20% per year.

Step 2: Initial Value Identification

The computer's initial value is given as $2500. This will be used as the starting point in calculating depreciation over time.

Step 3: Depreciation for Year One

In the first year, the computer loses 20% of its value. Calculate the depreciation amount for the first year with the formula: \( ext{Depreciation} = ext{Initial Value} imes rac{ ext{Rate}}{100} \) which yields: \( 2500 imes 0.20 = 500 \)

Step 4: Value After One Year

Subtract the depreciation from the initial value to find the value at the end of year one: \( 2500 - 500 = 2000 \). So, the computer's value after one year is $2000.

Step 5: Depreciation for Year Two

In the second year, the computer's value depreciates again by 20% of the remaining $2000. Calculate the depreciation amount with the same formula:\( 2000 imes 0.20 = 400 \)

Step 6: Value After Two Years

Subtract the second year's depreciation from the value at the end of year one to find the value at the end of year two: \( 2000 - 400 = 1600 \). So, the computer's value after two years is $1600.

Key Concepts

Percentage

Depreciation involves understanding percentages, which are a way to express a number as a fraction of 100. In the context of depreciation, the percentage represents how much of the asset's value is lost over a particular period.
Let's break it down further:

• A 20% depreciation rate means that every year, the asset loses 20 out of every 100 units of its value.
• To find the depreciation, you multiply the asset's current value by 0.20 (because 20% as a decimal is 0.20).
• This calculation helps in determining the exact amount that should be subtracted from the asset's value each year.

So, if an asset worth \(2500 depreciates by 20% in the first year, you calculate the loss as follows:- Current Value = \)2500- Depreciation Amount = \(2500 \( \times \) 0.20 = \)500This shows a reduction of \(500 in the first year, resulting in a new value of \)2000.

Asset Value

The asset value is the worth of an asset at any given time. At the beginning, the computer's initial asset value is $2500.
As depreciation affects the asset, this value declines steadily. To keep track:

• Begin with determining the initial value, which is often the purchase price.
• Deduct the annual depreciation amount from the asset's current value to find its new value.

Consider how depreciation impacts the asset value over two years in the case of Zeus Industries: - **Initial Year**: The value starts at $2500. - **After Year One**: Depreciation of $500 reduces the value to $2000. - **After Year Two**: Another depreciation of $400 reduces it to $1600. Keep in mind, the asset value changes each year just like above, needing recalculation based on the previous year’s ending value.

Mathematical Formulas

Calculating depreciation is readily handled through straightforward mathematical formulas.
These formulas help organize and simplify finding how an asset's value changes over time.Key formula for finding depreciation amount:\[ \text{Depreciation} = \text{Current Asset Value} \times \frac{\text{Rate of Depreciation}}{100} \]This formula provides the depreciation expense for the year, reflecting how much value the asset has lost due to wear and tear or technological obsolescence.Example steps:1. **First Year**: - Current Value: \(2500 - Calculation: \( 2500 \times 0.20 = 500 \) - New Value: \)20002. **Second Year**: - Current Value: \(2000 - Calculation: \( 2000 \times 0.20 = 400 \) - New Value: \)1600Altogether, mathematical formulas bring clarity and repeatability to the processes required in evaluating the decreasing value of assets annually.