Problem 4 - 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.) Savings Account A local bank pays \(5.5 \%\) annual interest on all savings accounts. If \(\$ 600\) is invested in this type of account, how much will be in the account at the end of a year?

Step-by-Step Solution

Answer

The amount in the account after a year will be $633.

Step 1: Identify the Given Values

The problem states that the annual interest rate is 5.5%, and the principal amount (the initial amount of money) is $600. We need to find the total amount in the account at the end of one year, which includes both the principal and the interest earned.

Step 2: Convert the Percentage to Decimal

To use the interest formula, convert the interest rate from a percentage to a decimal. Divide 5.5 by 100 to get 0.055.

Step 3: Use the Simple Interest Formula

The formula for simple interest is: \[I = P \times r \times t\]where: \(I\) is the interest,\(P\) is the principal amount ($600),\(r\) is the annual interest rate (0.055),\(t\) is the time in years (1 year in this case).Plug in the values to find the interest: \[I = 600 \times 0.055 \times 1 = 33\]

Step 4: Calculate the Total Amount

To find the total amount in the account after one year, add the interest earned to the principal amount: \[A = P + I = 600 + 33 = 633\]

Step 5: Conclusion

The total amount in the account at the end of the year will be $633.

Key Concepts

Interest Rate Conversion

Understanding how to convert an interest rate from a percentage to a decimal is essential when calculating interest. This conversion is important because most mathematical formulas used in finance require interest rates in decimal form. To do this, simply divide the percentage by 100. For example, converting a 5.5% interest rate involves dividing 5.5 by 100, which results in 0.055.

• This decimal form fits into the simple interest formula effortlessly.
• Always perform this step before applying formulas to prevent errors.

This method not only applies to annual rates but can be used for any rate expressed as a percentage.

Savings Account

A savings account is a secure place to keep your money while earning interest over time. It offers financial growth without needing active investments.

• The bank pays interest on your savings, which increases your total amount.
• In the given example, a $600 investment earns interest in one year due to a 5.5% rate.

Savings accounts are also a great tool for emergency funds due to their liquidity. You can access your savings when needed, providing financial security.

Financial Literacy

Financial literacy involves understanding key financial concepts, like interest rates and savings strategies. It's crucial for making informed decisions about managing resources.

Educating yourself about savings accounts and interest calculations enhances your financial literacy. It empowers you to:

• Evaluate the benefits of different types of bank accounts.
• Choose the best interest rates for your needs.
• Plan for future expenses effectively.

Enhanced financial literacy leads to better financial stability and can help you achieve your monetary goals.

Mathematical Formulas

Mathematical formulas are tools that simplify complex calculations, breaking them into manageable steps. The simple interest formula, for example, is \[I = P \times r \times t\] where:

• \( I \) is the interest.
• \( P \) represents the principal sum.
• \( r \) is the rate of interest in decimal form.
• \( t \) is the time period.

This formula is straightforward and serves as a basis for more complex financial computations. Knowing how to use it with the correct values is key to accurately determining how much interest your savings will generate. Defining these terms clearly aids in understanding and applying the formulas efficiently.