Problem 22 - Elementary Algebra

Question

Use numerical evaluation on the equations. Business (simple interest) \(I=p r t . \) Find \(I\) if \(p=3000, r=.12\) and \(t=1 .\)

Step-by-Step Solution

Answer

Answer: The simple interest is $360.

Step 1: Write down the formula

We have the formula for simple interest as \(I = prt\).

Step 2: Substitute the given values into the formula

We are given \(p = 3000\), \(r = 0.12\), and \(t = 1\). Therefore, we can replace these values in the formula: \(I = (3000)(0.12)(1)\).

Step 3: Calculate the simple interest

Now, we will calculate the multiplication: \(I = 3000 \times 0.12 \times 1 = 360.\) So, the simple interest (I) of this business investment in one year is \(360\).

Key Concepts

Numerical Evaluation

Numerical evaluation is a fundamental skill in mathematics that involves substituting numbers into an algebraic equation or expression in order to find a specific value. In the context of the problem solved, numerical evaluation helps us compute the interest amount by replacing the general variables with the given numerical data.

In the given exercise, numerical evaluation begins once we understand the simple interest equation and identify the values provided:

• Principal (\(p\)): This is the initial amount invested or loaned, which in this case is \(3000\).
• Rate (\(r\)): The interest rate per time period, here represented as \(0.12\), or 12%.
• Time (\(t\)): The duration for which the principal is invested or borrowed, which is 1 year in this scenario.

By substituting these values into the formula, we can effectively evaluate the expression and determine the simple interest generated over the given time period.

Simple Interest Formula

The simple interest formula is a straightforward equation used in finance to calculate the interest that an investment or loan will earn or accumulate over a period of time.

The formula is expressed as \(I = prt\), where \(I\) represents interest, \(p\) is the principal amount, \(r\) is the rate of interest, and \(t\) is the time for which the money is invested or borrowed. This formula assumes that the interest rate is constant over the time period, and it does not include the effects of compound interest.

• Simplicity: This formula's simplicity makes it ideal for quick calculations without the need for complex financial tools.
• Applicability: It's especially useful in straightforward or short-term financial agreements where compound interest is negligible.

In our example, calculating the simple interest using this formula is a matter of plugging in the values provided, leading to an easy-to-understand calculation.

Business Mathematics

Business mathematics is a field that applies mathematical methods and models to solve real-world business problems, including financial calculations like simple interest.

Understanding simple interest is crucial in various business applications, especially in finance and banking:

• Loans and Investments: It helps in evaluating the cost of borrowing money and the potential return on investments.
• Budget Planning: Incorporating simple interest calculations aids businesses in planning future expenses and income.
• Financial Decision-Making: Being proficient in business mathematics supports sound financial decisions and strategy formulation.

The exercise provided is a basic yet practical example of how business mathematics apply numerical skills to calculate interest, aiding in financial planning and assessment. Simple interest problems offer a conceptual foundation that paves the way for understanding more complex financial instruments.