Question

For Exercises \(1-10\), calculate the simple interest and final balance. \(\$ 350\) at \(5.5 \%\) for 2 years

Short answer

Answer: The simple interest is $38.5, and the final balance after 2 years is $388.5.

Step-by-step solution

Convert the interest rate to a decimal

To convert the interest rate of 5.5% to a decimal, we will divide by 100: Interest Rate (decimal) \(= \frac{5.5}{100} = 0.055\)

Calculate the simple interest

Now we will use the simple interest formula: Simple Interest \(= P \times R \times T\) Substitute the principal amount (\(P = 350\)), interest rate (decimal, \(R = 0.055\)), and time in years (\(T = 2\)): Simple Interest \(= 350 \times 0.055 \times 2\) Calculate the result: Simple Interest \(= 38.5\)

Calculate the final balance

Add the principal amount and the simple interest to find the final balance: Final Balance \(= P + \text{Simple Interest}\) Final Balance \(= 350 + 38.5\) Calculate the result: Final Balance \(= 388.5\) The simple interest is \(38.5 and the final balance after 2 years is \)388.5.

Key concepts

Interest Rate Conversion

When dealing with simple interest, it's crucial to convert the interest rate from a percentage into a decimal form. This makes calculations easier and more straightforward. To perform this conversion, divide the percentage by 100. For example, an interest rate of 5.5% becomes a decimal by calculating \( \frac{5.5}{100} = 0.055 \). This decimal form is essential for further calculations in the simple interest formula.

• Step-by-step: Divide the percentage rate by 100.
• Essential for interest calculations.

This conversion is a foundational step that ensures accuracy and consistency in financial computations, removing complications that arise when dealing with percentages directly.

Principal Amount

The principal amount is the starting sum of money that either borrow or invest. In simple interest calculations, the principal remains constant throughout the period of investment or loan. This is because, unlike compound interest, the interest calculated does not get added back to the principal.

• Initial amount of money invested or loaned.
• In our example: \( \$350 \).

Understanding the principal is important as it serves as the base amount on which interest is calculated. The principal amount itself is not influenced by the interest rate or time.

Final Balance Calculation

Calculating the final balance involves adding the simple interest earned to the original principal amount. The formula used is: \( \text{Final Balance} = P + \text{Simple Interest} \).
In the given exercise, after calculating the simple interest as \( \\(38.5 \), you add this value to the principal (\( \\)350 \)), resulting in a final balance of \( \$388.5 \).

• Formula: Principal + Simple interest.
• Ensures full value at end of term.

This step is key to determining the total amount after the interest has been applied, providing a clear picture of the financial outcome over the specified period.

Time in Years

Time influences how interest accumulates, calculated in years for simple interest. This period dictates how long the interest will be earned. The longer the time, the more interest accumulates.
In our example, the time given is 2 years, which is directly used in the simple interest formula. This simple yet crucial element informs the length of the investment and plays a significant role in calculating total interest.

• Measured in years for simple interest calculations.
• Directly impacts total interest.

Time is a straightforward concept but vital for understanding how long an investment or loan will accrue interest, impacting financial planning and decision-making.