Calculating the Final Purchase Price with Discounts and Taxes

When making a purchase, it is important to understand how the final price can be calculated considering both discounts and taxes. This guide will walk you through the process step by step, ensuring you can accurately determine the final amount you will have to pay. Whether you are a business owner adjusting your pricing or a consumer shopping for deals, understanding these calculations can save you money and ensure transparency in financial transactions.

Step-by-Step Calculation Process

Let's break down the process of calculating the final purchase price, which includes determining the original price, applying discounts, and calculating the tax. Here’s how you can do it:

Determine the Original Price

The original price is the starting point for your calculations. This is the price of the item before any adjustments are made for discounts or taxes. To proceed, you need to identify this value accurately.

Calculate the Discount

Discounts can be expressed as a percentage. To calculate the discount amount, use the formula:

Discount Amount Original Price × (Discount Percentage / 100)

After determining the discount amount, subtract it from the original price to get the discounted price:

Discounted Price Original Price - Discount Amount

Calculate the Tax

Taxes are also expressed as a percentage. To find the tax amount, use the following formula:

Tax Amount Discounted Price × (Tax Percentage / 100)

Calculate the Final Purchase Price

To get the final purchase price, add the tax amount to the discounted price:

Final Purchase Price Discounted Price Tax Amount

Example Calculation

Let's go through an example to illustrate the process:

Original Price: $100 Discount: 20% Tax Rate: 8% Original Price: $100 Calculate the Discount Amount:

$100 × (20 / 100) $20

Calculate the Discounted Price:

$100 - $20 $80

Calculate the Tax Amount:

$80 × (8 / 100) $6.40

Calculate the Final Purchase Price:

$80 $6.40 $86.40

The final purchase price would be $86.40.

A Quick Algebraic Equation

You can simplify the process using an algebraic equation. Here's how the final price (X) is calculated:

P: Original Price d: Discount given as a decimal (e.g., 15% becomes 0.15) t: Taxes expressed as a decimal (e.g., 8% becomes 0.08) X: Final Price

P × (1 - d) × (1 t) X

Note: Always make sure to follow the algebraic order of operations.

Example Calculation Using the Algebraic Equation

Consider the example:

P $200 d 0.2 (20%) t 0.1 (10%)

$200 × (1 - 0.2) × (1 0.1) X

$200 × 0.8 × 1.1 X

$200 × 0.88 X

X $176

The final price (X) would be $176.

Conclusion

Understanding how to calculate the final purchase price with discounts and taxes is crucial for both businesses and consumers. By following these steps and utilizing the provided formulas, you can accurately determine the price you will have to pay. Remember to always verify the data and use the correct formatting to avoid any discrepancies. This knowledge can help you make informed decisions and save money in the long run.