Problem 49 - Prealgebra

Question

In \(1990,\) Congress passed a law, which took effect on January \(1,1991,\) requiring an additional tax of \(10 \%\) on a portion of the purchase price of certain luxury items. (In 1996 the law was amended so that this tax on luxury automobiles expired in 2003.) For expensive cars, it was paid on the part of the purchase price that exceeded 30,000 dollars. For example, if you purchased a Jaguar XJ-S for 53,000 dollars , you would pay a luxury tax of \(10 \%\) of 23,000 dollars , because the purchase price, 53,000 dollars , is 23,000 dollars above 30,000 dollars If you purchased a Jaguar XJ-S for $$ 53,000\( on February \)1,1991,\( in California, where the sales tax rate was \)6 \%$ how much would you pay in luxury tax and how much would you pay in sales tax?

Step-by-Step Solution

Answer

Luxury tax: $2,300; Sales tax: $3,180.

Step 1: Determine the Amount Subject to Luxury Tax

Since the luxury tax applies only to the amount exceeding \(30,000, subtract \)30,000 from the purchase price of $53,000 for the Jaguar XJ-S:\[ \text{Amount subject to luxury tax} = 53,000 - 30,000 = 23,000 \]

Step 2: Calculate the Luxury Tax

The luxury tax is 10% of the amount that exceeds \(30,000. Therefore, calculate 10% of \)23,000:\[ \text{Luxury tax} = 0.10 \times 23,000 = 2,300 \]

Step 3: Determine the Sales Tax Base

The sales tax applies to the entire purchase price, which is $53,000. Therefore, no adjustment is needed to the sales tax base.

Step 4: Calculate the Sales Tax

The sales tax rate in California is 6%. Calculate 6% of the entire purchase price of $53,000:\[ \text{Sales tax} = 0.06 \times 53,000 = 3,180 \]

Step 5: Sum Up Both Taxes

Finally, add both the luxury tax and the sales tax to find the total tax paid:\[ \text{Total tax} = \text{Luxury tax} + \text{Sales tax} = 2,300 + 3,180 = 5,480 \]

Key Concepts

Understanding Luxury Tax

Luxury tax is a type of tax imposed on particular items that are considered non-essential or luxury goods. These goods tend to be high-end items that command a hefty price, such as luxury cars, jewelry, or expensive boats. The main goal of the luxury tax is not only to generate revenue for governments but also to discourage excessive consumption by making these high-end items more expensive for consumers.
When you buy a luxury item, only the portion of the purchase price that exceeds a certain threshold is subject to this tax. For example, in 1991, a law was enforced in the U.S. that required a 10% luxury tax on the amount that exceeded $30,000 for luxury cars.

• The tax only applies to the portion of the price above the threshold.
• The rate of the luxury tax can vary based on the item and region.

Therefore, if a car costs $53,000, and the threshold is $30,000, you pay the tax only on $23,000, resulting in a luxury tax of $2,300. This type of taxation encourages consumers to think twice before purchasing pricey items.

Mastering Percentage Calculation

Calculating percentages is a vital math skill, particularly in the context of taxes. A percentage is essentially a fraction or a portion of 100. To determine a percentage, you typically multiply the given number by the percentage desired, expressed as a decimal.
For instance, if you need to calculate 10% of \(23,000, you would first convert the percentage to a decimal, which would be 0.10, and then multiply this by the amount:
\[ 0.10 \times 23,000 = 2,300 \]This calculation shows that \)2,300 is the amount of luxury tax on \(23,000. Similarly, to find 6% of the entire purchase price of \)53,000, simply convert 6% to 0.06 and multiply:
\[ 0.06 \times 53,000 = 3,180 \]Thus, $3,180 is the sales tax amount.

• Always convert the percentage to a decimal.
• Multiply the decimal by the total or relevant amount.

Mastering percentage calculations can help ensure correct tax computations.

Navigating Tax Laws

Tax laws are the rules and regulations set by the government to structure the tax system within a country or region. These laws determine how much tax is applied, which products or services are taxable, and any exemptions or special considerations for certain goods.
Sales tax and luxury tax are two different kinds of taxes regulated by these laws. While sales tax is a general tax applied to the sale of most goods and services, luxury tax specifically targets high-value items beyond a certain price point.

• Sales tax rate varies by state or region.
• Luxury tax targets only specified high-value goods.
• Understanding tax laws can help optimize purchasing decisions, especially for high-value transactions.

Staying informed about both types of tax can better equip consumers and businesses to plan and optimize their financial strategies. It’s essential to check the most current tax laws, as they can change over time, affecting how much tax one might owe on particular purchases.