Question

Personal Finance: cost of a Car The suggested list price of a new car is 24,000 dollar .\( The dealer's cost is \)85 \%$ of list. How much will you pay if the dealer is willing to accept 300 dollar over cost for the car?

Short answer

20700 dollars

Step-by-step solution

Find the Dealer's Cost

The dealer's cost is 85% of the list price. Calculate the dealer's cost by multiplying 24,000 dollars by 0.85.\[\text{Dealer's Cost} = 24000 \times 0.85 = 20400 \text{ dollars}\]

Add Dealer's Profit

The dealer is willing to accept 300 dollars over the cost price. Add this amount to the dealer's cost to find the total amount to be paid.\[\text{Total Amount to be Paid} = 20400 + 300 = 20700 \text{ dollars}\]

Key concepts

Understanding Cost Calculation

In personal finance, 'cost calculation' is an essential concept that helps you understand how much you need to spend. Cost calculation involves determining the actual price you'll end up paying for a product or service. In the context of this exercise, you start with the list price of a car, which is 24,000 dollars. However, the 'dealer's cost' is 85% of this list price. This means the dealer bought the car at a reduced price, which in this case is 20,400 dollars. To calculate this, you multiply 24,000 dollars by 0.85: \[\text{Dealer's Cost} = 24000 \times 0.85 = 20400\text{ dollars}\]Calculating costs correctly ensures you don't overspend, helping you make informed financial decisions.

Using Percentages in Calculations

Percentages are a way of expressing a number as a fraction of 100. They are very useful in finance and everyday math. In our car cost calculation, we see percentages in action. We know the dealer's cost is 85% of the list price. Here, 85% means 85 out of every 100. To find the dealer's cost, you use 85% of the list price. This is done by multiplying the list price by the percentage in its decimal form.In math, converting a percentage to a decimal is simple: you divide by 100. So, 85% becomes 0.85. You then multiply it with the list price of 24,000 dollars:\[24000 \times 0.85 = 20400\text{ dollars}\]Understanding how to handle percentages helps in many areas, including shopping discounts, calculating interest rates, and even determining your grades in school.

Calculating Dealer Profit

Dealer profit refers to the additional money a dealer makes above their costs. In this exercise, the dealer is selling the car for 300 dollars above their cost. To find out the total amount you will pay, you must add this dealer profit to the dealer's cost.First, we have the dealer's cost calculated as 20,400 dollars. Then, we add the dealer's profit of 300 dollars:\[20400 + 300 = 20700\text{ dollars}\]So, the total price you will pay for the car is 20,700 dollars. Knowing how dealer profit works helps you understand negotiations and ensures you don't pay unnecessary add-ons.

Real-World Math Applications

Math isn't just about numbers on a page; it's used every day in real-world scenarios. Understanding concepts like cost calculation, percentages, and profit helps in various financial decisions. Whether you're buying a car, shopping for groceries, or planning a budget, these concepts are crucial.For example:

• Cost Calculation: Helps you determine the final price of an item considering discounts or additional fees.
• Percentages: Useful in calculating interest rates for loans, tips at restaurants, and markdowns during sales.
• Dealer Profit: Knowing this helps in negotiating better deals when making large purchases.

Applying these real-world math skills ensures that you manage your finances better and make informed purchasing decisions.