Grades 9-12

# Interest and Parent Growth

### Objective

Students will be able to:

- Describe how interest on loans and investments work.
- Calculate interest over a specific period of time.
- Use proportional relationships to solve problems related to percent increase/decrease.

In this math lesson, students will examine and calculate interest on loans and investments.

### Resources

### Procedure

Warm-Up

Ask students what they know about interest rates. (Answers will vary.) Tell them this lesson is designed to help them understand the “math” behind interest rates so they can make more informed decisions when borrowing and investing money. Open up the Resource Slides and show Slide 2. Have students read through the problem and discuss it. You may choose to have them participate in pairs, in groups, or as the whole class. After students have completed their discussions and reached a conclusion, tell them there is no wrong answer to the question. Explain that Option 1 is viewed as a better deal if they compared the rate of return ($5 is a 5% rate of return on $100 and $9 is a 4.5% rate of return on $200). However, Option 2 is a better deal if they compared the total ($105 is less than $109).

Show Slide 3. Tell students the same principle applies to the answers here. They may choose to select multiple trolls for their investments with either Option 1 or Option 2. Be sure students understand both arguments. Remind them both types of reasoning are mathematically correct, but there may be a preferred strategy when dealing with their own personal finances.

Modeling

Tell students this lesson will help them understand how percentages relate to interest rates, and how those interest rates affect their decisions when investing or borrowing money.

Explain that the troll’s offer is similar to how banks and financial institutions operate when they are lending money or providing investment opportunities for consumers. Tell students that interest rates can vary greatly, depending upon a variety of circumstances such as the length of time.

Show Slide 4. Tell students that people invest to earn interest on their money. Review the terms, explaining that people earn interest when they invest, but pay interest when they borrow. Distribute Worksheet 1 Introduction to Interest and go over the instructions, showing students how to use the lesson’s vocabulary and calculate percentages. (Note: You may want to work through the first example to demonstrate the assignment. You may choose to put students in small groups or work on their own.) When students have completed the problems, have them share their answers with another group or partner. Review their answers using Worksheet 1 Answer Key. Address any questions or concerns about the problems before proceeding. Distribute Worksheet 2 Interest and Percent Growth and review the instructions. Tell students the problems in this worksheet build on the concepts in Worksheet 1 by adding principal to the activity. (Note: You may want to work through the first example to demonstrate the assignment. You may choose to put students in small groups or work on their own.) When students have completed their work, review their answers with the class using Worksheet 2 Answer Key. Address any questions or concerns about the problems before proceeding.

Show Slide 5. Explain that principal can be used as a percent (100% of the principal), which allows them to calculate the equations. Use questions #4 and #5 from Worksheet 2 Interest and Percent Growth to facilitate a discussion of two strategies.

Show Slide 6. Highlight that the principal can be described as a percent, 100% of the principal. Describe the two ways students can find total money after one year: a. they can add the interest rate to 100% (r%+100%) because both percents are describing parts of the same whole; remind them that they can only add percents when describing parts of the same whole; applying the total percent (r%+100%) to the principal will result in the total dollars. b. they can find the part of the whole principal r% described in dollars and add the quantity to the principal given in dollars. In this case, the quantities being added are given in dollars. (Note: It may also be helpful to show students why both strategies work using the distributive property.)

NOTE: For a deeper dive into calculating interest, visit lessons The Benefits of Investing Early or Compound Interest and Your Financial Lifecycle.

Group Activity

Put students into small groups, saying they will be working in their groups to calculate two situations: percent increases and percent decreases. Distribute copies of Worksheet 3 Percent Increases and give them ten minutes to complete the questions. (Note: It is important to tell students that a 30 percent increase in one year in any investment is very unlikely. Explain that it is being used ONLY to illustrate a large gain but is not a realistic expectation. In fact, they might want to beware of a scam or fraud that would promise them an excessive return on their investment.) Review their answers using Worksheet 3 Percent Increases Answers and tell them they will now calculate decreases. Distribute copies of Worksheet 4 Percent Decreases and give them ten minutes to complete the questions. Review their answers using Worksheet 4 Percent Decreases Answers.

Individual Activity

Tell students they will be working individually to solve some additional problems using percent and applying all they have learned in the previous exercises. Distribute copies of Worksheet 5 Problem Sets. (Note: the problems in this worksheet may be more challenging for students to complete. You may want to let students know that it is okay if they are confused or struggle to answer the questions and assure them you will be reviewing the problems with them.) Give students a limited amount of time to complete the worksheet and review the problems using the Worksheet 5 Problem Sets Answers (Note: You may want to conclude this lesson by reviewing the terms and reminding students that this lesson is only a brief overview of the role math plays in borrowing, lending, and interest rates.)

### Assessment

Show Slide 7. Have students complete the following assignment: Create three questions on percent increase/decrease similar to those in today’s lesson. At least one question must be related to interest. Include the answers to your questions. Use appropriate terms/vocabulary in your questions and answers. (Answers will vary.)

## Related Resources

Grades 6-8, 9-12

### Compound Interest Calculator

Grades 9-12

### On Demand Thursdays: A.P. Fundamentals: Scarcity

Content Partner

Grades 9-12