Question

Josephine purchases a computer for \(\$ 4,590\). The computer decreases in value at a constant rate for 9 years, after which it is considered not to have any monetary value. How much is the computer worth 6 years after it is purchased? A) \(\$ 1,530\) B) \(\$ 2,295\) C) \(\$ 3,060\) D) \(\$ 4,080\)

Short answer

A) \(\$ 1,530\)

Step-by-step solution

Determine the annual depreciation of the computer

In order to find out how much the computer is worth after 6 years, we first need to determine its annual depreciation. To do this, we will divide the initial value of the computer (\(\$4,590\)) by the number of years it takes for it to become worthless (9 years). The formula for annual depreciation is: Annual Depreciation = \(\frac{\text{Initial Value}}{\text{Number of Years}}\)

Calculate the annual depreciation

Plugging the values into the formula from Step 1, we have: Annual Depreciation = \(\frac{\$4,590}{9}\) Annual Depreciation = \(\$ 510\) The computer loses \(\$510\) in value each year.

Determine the value of the computer 6 years after it is purchased

Now that we know the annual depreciation, we can find the computer's value after 6 years. To do this, we will multiply the annual depreciation by the number of elapsed years (6) and subtract that amount from the initial value of the computer. The formula for the computer's value after 6 years is: Value after 6 years = Initial Value - (Annual Depreciation × 6 years)

Calculate the value of the computer after 6 years

Plugging the values into the formula from Step 3, we have: Value after 6 years = \(\$4,590\) - (\(\$510\) × 6) Value after 6 years = \(\$4,590\) - \(\$3,060\) Value after 6 years = \(\$1,530\) After 6 years, the computer is worth \(\$1,530\). Therefore, the correct answer is: A) \(\$ 1,530\)

Key concepts

Annual Depreciation Calculation

Understanding annual depreciation is crucial for students who are dealing with real-life scenarios involving asset management or taking standardized tests like the SAT. It's a measure of how much an asset, like Josephine's computer, loses value over the course of a single year due to wear and tear, usage, or obsolescence.

To calculate annual depreciation, you need two key pieces of information: the initial value of the asset and the lifespan over which the asset depreciates. The formula is relatively simple and can be expressed as follows: \[\begin{equation}Annual Depreciation = \frac{Initial Value}{Number of Years}\end{equation}\]By using this formula, we discovered that the computer depreciates by \(\$510\) each year.

For students practicing SAT math or facing similar depreciation problems, it's essential to get comfortable with this formula. You often have to perform these calculations under time constraints, so remember to practice until the method becomes second nature. This will ensure quick and correct responses during tests.

Value Depreciation Math

Now, let's delve deeper into value depreciation math from our previous example. After finding out the annual depreciation, we need to assess the value of the asset after a certain time has passed. The general formula we use is: \[\begin{equation}Value after X years = Initial Value - (Annual Depreciation \times X years)\end{equation}\]This formula helps determine the depreciated value after any number of years. Following this method, we computed that Josephine's computer would be worth \(\$1,530\) after 6 years.

It's essential to practice these calculations not just for textbook exercises but also for real-world applications in the fields of finance, accounting, and even purchasing decisions for personal assets. Students can enhance their understanding of depreciation by applying this math to various scenarios, preparing them for both academic assessments and practical financial literacy.

SAT Math Practice

When it comes to SAT math practice, solving depreciation problems is a valuable skill. It requires a good grasp of algebra and the ability to perform calculations with precision. Practice problems may involve assets such as electronics, vehicles, or machinery, and they test your understanding of linear value decrease over time.

For effective SAT math practice, always start by carefully reading the problem to identify what is being asked. Next, apply the relevant formulas, as we did with Josephine's computer, and simplify your calculations where possible. Here, we used: \[\begin{equation}Annual Depreciation = \frac{Initial Value}{Number of Years}\end{equation}\]And then: \[\begin{equation}Value after X years = Initial Value - (Annual Depreciation \times X years)\end{equation}\]Remember, practice is key — work on a variety of depreciation problems to solidify the concept. The SAT might challenge you with different variables, so understanding the underlying principles is crucial. Furthermore, mastering these types of problems can boost your confidence and speed on test day, contributing to a better overall performance.