Problem 28 - Elementary Algebra

Question

Use numerical evaluation to evaluate the equations for the following problems. $$ I=\text { prt. } \quad \text { Find } I \text { if } p=1000, r=0.06, \text { and } t=3 \text { . } $$

Step-by-Step Solution

Answer

Answer: The simple interest (I) is 180.

Step 1: Identify the given values

We are given the following values: Principal amount (p) = 1000 Interest rate (r) = 0.06 Time period (t) = 3

Step 2: Use the simple interest formula

The formula for simple interest is I = prt. We will substitute the given values of p, r, and t into this formula to find the interest (I).

Step 3: Substitute the given values into the formula

Substitute the given values into the simple interest formula: I = (1000)(0.06)(3)

Step 4: Calculate the interest

Now, we will multiply the numbers together to find the interest: I = 1000 * 0.06 * 3 = 60 * 3 I = 180

Step 5: State the final answer

The interest (I) is 180 when the principal amount (p) is 1000, the interest rate (r) is 0.06, and the time period (t) is 3 years.

Key Concepts

Numerical Evaluation

Numerical evaluation is a method used to compute the values of expressions by substituting numerical values for variables. It is the first step that plays a crucial role when dealing with mathematical formulas, especially in finance.

For instance, when determining simple interest, we use the formula I = prt, where I stands for interest, p for principal amount, r for interest rate, and t for time. Through numerical evaluation, we assign real numbers to these variables and then perform the multiplication. This operation transforms the abstract formula into a tangible result, reflecting how much interest is accrued over time. By accurately assessing each variable and substituting it into the formula, we ensure correct results.

Simple Interest Calculation

The calculation of simple interest is a fundamental concept in finance that determines the additional amount owed on a loan or earned on an investment based solely on the initial principal. To perform a simple interest calculation:

• Identify the principal amount (the initial sum of money).
• Determine the annual interest rate (expressed as a decimal).
• Decide the time period (often measured in years).

Once these values are ascertained, multiplying them together yields the simple interest. For our exercise, when the principal is \(1000, the rate is 6%, and the time is 3 years, the simple interest accrues to \)180 using I = prt.

Interest Rate

The interest rate is the percentage charged on the principal amount over a specific period of time, typically one year, and is a critical factor in financial transactions. It can be expressed either as a percentage or a decimal, with the latter being used in calculations. For our problem, an annual interest rate of 0.06 (or 6%) is given. This rate determines how much money will be paid in interest on the principal sum each year.

Understanding how to convert and use this rate in calculations is key to not only solving interest problems but also to making informed financial decisions, be it evaluating loans or investment opportunities.

Principal Amount

The principal amount refers to the initial sum of money on which interest is calculated. It is essentially the starting figure before any interest is added or accrued over time. In financial terms, it is the original investment or loan amount.

In the context of our example, the principal amount is $1000. This is the foundation upon which we calculate our simple interest, and it is crucial to accurately identify this amount to determine the correct interest earned or owed over a specified period. The principal is the 'p' in the simple interest formula I = prt, which signifies its central role in the calculation of interest.