Problem 23 - Elementary Algebra

Question

Use numerical evaluation on the equations. Business (simple interest) \(I=p r t . \) Find \(I\) if \(p=250, r=0.07\) and \(t=6\).

Step-by-Step Solution

Answer

Question: Calculate the simple interest earned on a principal amount of $250 with an interest rate of 0.07 for 6 years. Answer: The simple interest earned is $105.

Step 1: Write down the given values

We have the following values: Principal amount (p) = 250 Interest rate (r) = 0.07 Time (t) = 6

Step 2: Substitute the values into the simple interest formula

Using the formula \(I = prt\), plug in the given values: \(I = (250)(0.07)(6)\)

Step 3: Perform the multiplication

Now, multiply the numbers together: \(I = (250)(0.07)(6) = 250 × 0.07 × 6 = 105\)

Step 4: Write the final answer

The simple interest (I) is 105. Therefore, the interest earned is $105.

Key Concepts

Numerical Evaluation

Numerical evaluation is the process of substituting numerical values into an expression and performing the calculations to arrive at a numerical result. This technique is commonly used in various mathematical problems, including finance and interest calculations.

Let's go through how we use numerical evaluation with the given problem. First, we identified the numerical values for the principal amount, interest rate, and time, which are respectively $250, 0.07, and 6 years. These values were then substituted into the simple interest formula (I = prt). After replacing the variables with our known numbers, we performed the actual multiplication - a process called numerical evaluation - to calculate the interest.

By understanding each step, students can dissect any formula and apply numerical evaluation confidently to solve similar problems. Breaking down the process and ensuring each operation is correctly performed are key components to mastering numerical evaluation in math.

Simple Interest Formula

The simple interest formula is a fundamental concept in finance that is used to calculate the interest earned or paid on a principal amount over a certain period. The formula is expressed as (I = prt), where I represents the interest amount, p is the principal amount, r is the interest rate, and t is the time in years.

To use the formula effectively, one must first understand what each variable signifies. The principal amount, p, is the initial sum of money loaned or invested. The interest rate, r, is typically expressed as a decimal, representing a percentage of the principal. Time, t, is usually counted in years for simple interest calculations. This formula is an indispensable tool for calculating interest in basic financial scenarios, and students should familiarize themselves with its structure and application method to be successful in business math.

Interest Calculation Math

Interest calculation is a critical component of financial mathematics, involving methodologies to figure out the cost of using borrowed money or the profit gained from money that is lent out. There are two main types of interest calculations: simple interest and compound interest.

Simple interest, as discussed in our exercise, is calculated on the original principal only, which makes it straightforward and easy to compute. In contrast, compound interest is calculated on the principal amount as well as on the interest accumulated over previous periods. While our focus here is on simple interest, understanding both types is important for a complete grasp of interest calculation math.

By mastering interest calculation techniques, students can apply these skills in various real-world scenarios, such as saving for retirement, taking out loans, or making investments. Enhancing one's ability in interest calculations can lead to more informed financial decisions and a better understanding of how money grows over time.