Problem 37 - 1,001 GED Practice Questions For Dummies

Question

Arnold invested \(700 in a savings account. After one year, his account balance was \)726.25. What percent annual interest did his bank pay?

Step-by-Step Solution

Answer

The annual interest rate the bank paid to Arnold is 3.75%.

Step 1: Calculate the interest amount

To find out the interest amount Arnold received, we need to subtract the initial investment from the account balance after one year: Interest amount = Account balance after one year - Initial investment Interest amount = \(726.25 - \)700

Step 2: Find the interest amount

Now, we calculate the interest amount: Interest amount = $26.25

Step 3: Calculate the annual interest rate

To find the annual interest rate, we need to determine the ratio of the interest amount to the initial investment. We can express this ratio as a percentage to find the annual interest rate: Annual interest rate = (Interest amount / Initial investment) * 100 Annual interest rate = (\(26.25 / \)700) * 100

Step 4: Calculate the annual interest rate

Now, we can calculate the annual interest rate: Annual interest rate = (26.25 / 700) * 100 Annual interest rate = 3.75% Thus, the bank paid an annual interest rate of 3.75%.

Key Concepts

Understanding Interest Calculation

Calculating interest is a fundamental skill in financial literacy. It helps you determine how much extra money you'll earn on an investment or pay on a loan. The basic formula to calculate simple interest requires three components:

• Principal (initial investment or loan amount)
• Interest rate (the percentage of the principal charged as interest)
• Time period (how long the interest is applied)

Simple interest is calculated using the formula: \[\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]Arnold's example helps illustrate this. His principal was \(700, with an earned interest amount of \)26.25 after one year. By rearranging the formula or manually computing as done in the exercise, our goal is to find the percentage, which sheds light on the next core concept—the annual interest rate.

Decoding the Annual Interest Rate

The annual interest rate is a reflection of how much interest an account earns or a loan accrues in one year. It is calculated by expressing the interest earned as a percentage of the principal amount invested. In Arnold's case, the steps were as follows:

After calculating the interest amount (\(26.25), we need to find out what percentage that amount represents of the original \)700. The formula used is:\[\text{Annual Interest Rate} = \left( \frac{\text{Interest Amount}}{\text{Principal}} \right) \times 100\%\]Hence for Arnold:\[\text{Annual Interest Rate} = \left( \frac{26.25}{700} \right) \times 100\% = 3.75\%\]This shows that the bank offered an annual interest rate of 3.75%. Understanding this percentage helps compare different investment opportunities or savings plans.

Building Financial Literacy

Financial literacy is the capability to understand and effectively manage various financial skills. This includes the concept of interest calculation, interpreting annual interest rates, and making informed decisions based on these calculations. Simple interest is just one part of this broad skill.

Being financially literate empowers you to:

• Understand how much you'll gain from investments.
• Know how loan interest can affect repayment amounts.
• Compare different financial products to choose the best ones.

Arnold's scenario gives a glimpse into how this knowledge translates into real-life decisions. Knowing how to calculate and interpret these numbers helps ensure you make sound financial decisions that best suit your goals. By mastering simple interest calculations, you can develop a stronger foundation for more complex financial concepts in the future.