Problem 9 - Prealgebra

Question

A These problems are similar to the examples found in this section. They should be set up and solved in the same way. (Problems 1-12 involve simple interest.) Student Loan A student takes out an emergency loan for tuition, books, and supplies. The loan is for \(\$ 600\) with an annual interest rate of \(5 \% .\) How much interest does the student pay if the loan is paid back in 60 days?

Step-by-Step Solution

Answer

The student pays approximately \( \$4.93 \) in interest.

Step 1: Understand the Variables

Begin by identifying the known variables in the simple interest formula. Here, the principal amount, \( P \), is \( \$600 \), the annual interest rate, \( r \), is \( 5\% \) (or 0.05 in decimal form), and the time, \( t \), is 60 days.

Step 2: Convert Time into Years

Since the interest rate is annual, convert the time from days to years because there are 365 days in a year. This step is important to maintain consistency with units. So, \( t = \frac{60}{365} \approx 0.1644 \text{ years} \).

Step 3: Use the Simple Interest Formula

The formula for simple interest is \( I = P \times r \times t \). Substitute the values from Step 1 into the formula: \( I = 600 \times 0.05 \times 0.1644 \).

Step 4: Calculate the Interest

Perform the multiplication to find the interest amount. \( I = 600 \times 0.05 \times 0.1644 = 4.932 \).

Step 5: Round to the Nearest Cent

Since we deal with money, round the interest to the nearest cent. Therefore, \( I \approx 4.93 \).

Key Concepts

Student Loan Interest

Student loans are often a part of college life, providing financial assistance to students to cover tuition and other essential expenses. One common aspect of loans is the interest you need to pay. Interest is the cost of borrowing money, and understanding how it's calculated can help you manage your finances better.

• The interest for student loans begins to accumulate from the time the money is loaned until it is fully repaid.
• Each loan has specific terms, and understanding these terms is crucial to compute the total cost you expect to pay.
• For our example, the student borrowed $600 at a 5% annual interest rate.

Borrowers should always be aware of the interest rate because even a small percentage can significantly affect the loan's cost over time.

Interest Calculation

To calculate simple interest, you use a straightforward formula: \[ I = P \times r \times t \]where:

• \( I \) is the interest amount,
• \( P \) is the principal (the original loan amount),
• \( r \) is the annual interest rate (in decimal form),
• and \( t \) is the time in years.

In our example, the time involved is 60 days, so it's necessary to convert this period into years to match the annual rate. You do this by dividing the number of days by 365 days a year: \[ t = \frac{60}{365} \approx 0.1644 \text{ years} \]Then, substitute these values into the formula to get the interest accrued over the 60 days. This calculation helps to determine exactly how much the student will need to pay just for borrowing the money.

Mathematical Problem Solving

Math can sometimes feel daunting, especially with financial computations, but breaking down problems into steps can make it manageable.

• First, identify what you're solving for and gather all the necessary information, such as principal, rate, and time.
• Converting all terms to consistent units is crucial. Here, changing days into years keeps everything on the same time scale.
• Use the simple interest formula, clearly laying out each step as you substitute the values.

Using a calculator can ease the arithmetic part of the problem, but understanding each step is key to effectively managing personal finances or tackling similar math problems. Following these steps, you'll find the interest amount, which can then be rounded appropriately when dealing with currency.