Problem 51 - Prealgebra

Question

Use any of the methods developed in this chapter to solve them. Student credit-card debt is at an alltime high. Consolidated Credit Counseling Services Inc. reports that \(20 \%\) of all college freshman got their first credit card in high school and nearly \(40 \%\) sign up for one in their first year at college. Suppose your credit card company charges \(1.3 \%\) in finance charges per month on the average daily balance in your credit card account. If your average daily balance for this month is \(\$ 2,367.90\) determine the finance charge for the month.

Step-by-Step Solution

Answer

The finance charge for the month is \(\$30.78\).

Step 1: Identify the given information

You are given the following information: the finance charge rate per month is \(1.3\%\), and the average daily balance for this month is \(\$2,367.90\).

Step 2: Convert the percentage to a decimal

To calculate the finance charge, first convert the percentage rate to a decimal by dividing by \(100\). Thus, \(1.3\%\) becomes \(0.013\).

Step 3: Calculate the finance charge

Multiply the average daily balance by the decimal finance charge rate to find the finance charge for the month: \(2,367.90 \times 0.013 = 30.7827\).

Step 4: Round to the nearest cent

Since financial amounts should be rounded to the nearest cent, round \(30.7827\) to two decimal places, resulting in \(30.78\). Thus, the finance charge for the month is \(\$30.78\).

Key Concepts

Percentage Calculation

Calculating percentages is a fundamental skill in many math-related concepts, including finance and business. In simple terms, a percentage is a way of expressing a number as a fraction of 100. This makes it easy to compare different quantities directly. For example, saying 20% means 20 out of every 100 units. When you need to calculate a percentage of a given number, you'll multiply the number by the percentage (as a decimal) to find the result.

Here's a quick guide:

• Identify the percentage and the base number.
• Convert the percentage to a decimal by dividing it by 100. For example, 1.3% becomes 0.013.
• Multiply the base number by the decimal. So, 2,367.90 × 0.013 = 30.7827.

Rounding to two decimal places gives a final finance charge of $30.78. Understanding percentage calculations helps in determining critical amounts such as finance charges, taxes, and discounts.

Decimal Conversion

Conversion from percentages to decimals is crucial in making calculations simpler. Percentages, though wildly useful, often require conversion to decimals to perform mathematical operations like multiplication or division.

Here's how you do it:

• Take the percentage value and divide it by 100. For example, to convert 1.3% to a decimal, divide 1.3 by 100 to get 0.013.
• This conversion allows more straightforward calculations, particularly when computing values such as finance charges, interest, or discounts.

Using decimals avoids the extra step of rearranging your equation to handle percentage signs and helps maintain precision in financial computations.

Financial Literacy

Financial literacy involves understanding and effectively using various financial skills, including personal financial management, budgeting, and investing. It's essential for making smart decisions about money and avoiding common financial pitfalls.

Key aspects of financial literacy include:

• Understanding how credit cards work, including how finance charges are calculated.
• Recognizing the importance of responsible credit use and staying aware of interest rates.
• Being able to calculate and understand the effects of finance charges, such as those calculated in the example, can help manage card balances and avoid unnecessary costs.

The knowledge gained from learning about these small calculations can assist in managing overall financial health and planning.

Interest Calculation

Calculating interest is a significant part of both personal and business finance. Interest is essentially the cost of borrowing money or, conversely, the reward for investing it. In the context of credit cards, interest calculations often involve multiplying the outstanding balance by the monthly finance charge or interest rate.

Here's a basic process:

• Identify the principal amount. For a credit card, this would be the unpaid balance.
• Determine the interest rate applicable, usually expressed as a percentage.
• Convert the percentage to a decimal (for instance, 1.3% becomes 0.013).
• Multiply the principal by the decimal interest rate to find the amount of interest due.

In our exercise, multiplying the outstanding balance of $2,367.90 by 0.013 gave us an interest amount of $30.78 for the month. By understanding interest calculations, individuals can better plan for managing debts and taking advantage of interest from savings or investments.