Stove Purchase Profit Calculation Understanding Discounts And VAT

In this article, we will delve into a mathematical problem involving the marked price of a stove, discounts, VAT (Value Added Tax), and profit/loss calculations. The scenario revolves around Heidi, who purchases a stove with cash and subsequently sells it to a friend. Our objective is to determine the profit or loss Heidi incurs in this transaction. This problem incorporates several key mathematical concepts, including percentages, discounts, VAT calculations, and profit/loss analysis. Understanding these concepts is crucial for solving real-world financial problems and making informed decisions in personal and business contexts.

The marked price of a stove is $8400. A discount of 33 1/3% is given on cash purchases. VAT at 12 1/2% has to be added to the discounted price. Heidi bought the stove with cash and sold it to a friend for $8150. How much profit or loss did she make?

To solve this problem, we need to break it down into several steps. First, we will calculate the discount amount on the stove's marked price. Then, we will subtract the discount from the marked price to find the price after the discount. Next, we will calculate the VAT amount on the discounted price and add it to the discounted price to find the final price Heidi paid for the stove. Finally, we will compare the price Heidi paid with the price she sold the stove for to determine her profit or loss.

1. Calculating the Discount

The discount given on cash purchases is 33 1/3%, which can be expressed as a fraction: 33 1/3% = 100/3 % = 1/3. To find the discount amount, we multiply the marked price by the discount rate:

Discount = (1/3) * $8400 = $2800

Therefore, the discount amount is $2800.

2. Calculating the Price After Discount

To find the price after the discount, we subtract the discount amount from the marked price:

Price after discount = Marked price - Discount Price after discount = $8400 - $2800 = $5600

So, the price of the stove after the discount is $5600.

3. Calculating the VAT Amount

VAT (Value Added Tax) is applied to the discounted price. The VAT rate is 12 1/2%, which can be expressed as a fraction: 12 1/2% = 25/2 % = 1/8. To find the VAT amount, we multiply the discounted price by the VAT rate:

VAT = (1/8) * $5600 = $700

Thus, the VAT amount is $700.

4. Calculating the Final Price Heidi Paid

To find the final price Heidi paid, we add the VAT amount to the discounted price:

Final price = Price after discount + VAT Final price = $5600 + $700 = $6300

Therefore, Heidi paid $6300 for the stove.

5. Calculating Profit or Loss

To determine Heidi's profit or loss, we compare the price she paid for the stove with the price she sold it for. She sold the stove for $8150, and she bought it for $6300.

Profit/Loss = Selling price - Cost price Profit/Loss = $8150 - $6300 = $1850

Since the result is positive, Heidi made a profit of $1850.

Marked Price

The marked price, also known as the list price or retail price, is the price at which a product or service is initially offered for sale. It is the price displayed on the product or advertised to potential customers before any discounts or taxes are applied. The marked price serves as a reference point for pricing negotiations and allows businesses to offer discounts or promotions while still maintaining a perceived value for the product.

In this problem, the marked price of the stove is $8400. This is the initial price at which the stove was offered for sale. The marked price is an important starting point for our calculations, as it is the basis for determining the discount amount and the final price paid by Heidi.

Discount

A discount is a reduction in the original price of a product or service. Discounts are often offered to customers for various reasons, such as to promote sales, clear out excess inventory, or reward customer loyalty. Discounts can be expressed as a percentage of the original price or as a fixed amount.

In this problem, a discount of 33 1/3% is given on cash purchases. This means that customers who pay in cash receive a reduction of 33 1/3% from the marked price. Discounts play a crucial role in attracting customers and increasing sales volume. By offering a discount, the seller makes the product more affordable and appealing to potential buyers.

VAT (Value Added Tax)

VAT (Value Added Tax) is a consumption tax levied on the value added to goods and services at each stage of the supply chain. It is a type of indirect tax, meaning that it is collected from businesses rather than directly from consumers. However, the cost of VAT is typically passed on to consumers in the form of higher prices. VAT is a significant source of revenue for many governments around the world.

In this problem, VAT at 12 1/2% has to be added to the discounted price. This means that after the discount is applied, the VAT is calculated on the discounted price and added to it to arrive at the final price. VAT is an important consideration for both businesses and consumers, as it affects the final cost of goods and services.

Profit and Loss

Profit is the financial gain realized when revenue exceeds expenses, while loss occurs when expenses exceed revenue. In the context of buying and selling goods, profit is the difference between the selling price and the cost price, where the selling price is the price at which the item is sold, and the cost price is the price at which the item was purchased. If the selling price is higher than the cost price, a profit is made. If the selling price is lower than the cost price, a loss is incurred.

In this problem, we calculate Heidi's profit or loss by comparing the price she paid for the stove ($6300) with the price she sold it for ($8150). Since the selling price is higher than the cost price, Heidi made a profit. The amount of profit is the difference between the selling price and the cost price, which is $1850.

Let's consider an alternative approach to solving this problem. Instead of calculating the discount and VAT separately, we can combine them into a single calculation. First, we calculate the effective price after the discount, which is (1 - 1/3) = 2/3 of the marked price. Then, we calculate the final price after adding VAT, which is (1 + 1/8) = 9/8 of the discounted price. Combining these calculations, the final price is (2/3) * (9/8) * $8400. Simplifying, we get (3/4) * $8400 = $6300, which is the same as the final price we calculated earlier. This alternative approach can be more efficient in certain situations.

In conclusion, by carefully analyzing the problem and breaking it down into smaller steps, we have determined that Heidi made a profit of $1850 in this transaction. This problem demonstrates the importance of understanding mathematical concepts such as percentages, discounts, VAT, and profit/loss calculations. These concepts are essential for making informed financial decisions in various real-world scenarios. Understanding how discounts and VAT affect the final price of goods and services can help consumers make better purchasing decisions. Similarly, businesses need to understand these concepts to accurately price their products and calculate their profits.

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