key term - Simple Interest

Definition

Simple interest is a method of calculating the amount of interest earned on a loan or investment, where the interest is calculated based on the principal amount, the interest rate, and the time period, without taking into account any compounding effects.

5 Must Know Facts For Your Next Test

1. The formula for calculating simple interest is: $I = P \times r \times t$, where $I$ is the interest, $P$ is the principal, $r$ is the interest rate, and $t$ is the time period.
2. Simple interest is often used in applications involving percent, such as calculating the amount of tax or tip on a purchase.
3. In mixture problems, simple interest can be used to determine the composition of a mixture, such as the ratio of ingredients in a solution.
4. Simple interest is a linear function, where the interest earned increases proportionally with the time period and the principal amount.
5. Unlike compound interest, simple interest does not take into account the compounding effect, where the interest earned on the interest also earns interest.

Review Questions

• Explain how the simple interest formula is used to solve percent applications.
  • In percent applications, the simple interest formula can be used to calculate the amount of tax, tip, or other percentage-based charges on a purchase. For example, if the principal amount is the pre-tax price of an item and the interest rate is the tax rate, the simple interest formula can be used to determine the total cost of the item including the tax. Similarly, the simple interest formula can be used to calculate the tip amount based on the pre-tax bill and the tip percentage.
• Describe how simple interest can be applied in mixture problems.
  • In mixture problems, simple interest can be used to determine the composition of a mixture, such as the ratio of ingredients in a solution. For example, if a mixture contains two different solutions with different concentrations, the simple interest formula can be used to calculate the relative amounts of each solution needed to create the desired concentration of the final mixture. The principal amount would represent the total volume of the mixture, the interest rate would represent the concentration of one of the solutions, and the time period would represent the proportion of that solution in the final mixture.
• Analyze the key differences between simple interest and compound interest, and explain how these differences impact the calculation of interest earned over time.
  • The primary difference between simple interest and compound interest is that compound interest takes into account the interest earned on the interest itself, whereas simple interest does not. This means that with compound interest, the amount of interest earned grows exponentially over time, while with simple interest, the interest earned grows linearly. As a result, the total amount of interest earned over a given time period will be higher with compound interest than with simple interest, especially for longer time periods. This has important implications for financial planning and decision-making, as the choice between simple or compound interest can significantly impact the overall return on an investment or the cost of a loan.

Related terms

Principal:

The initial amount of money borrowed or invested, on which interest is calculated.

Interest Rate:

The percentage of the principal amount charged or earned as interest over a specific time period.

Time Period: The duration for which the principal amount is borrowed or invested, typically expressed in years or months.