Interest and Percent 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.
Standard
Standard: 5
- Students will understand that: Credit allows people to purchase and enjoy goods and services today, while agreeing to pay for them in the future, usually with interest. There are many choices for borrowing money, and lenders charge higher interest and fees for riskier loans or riskier borrowers. Lenders evaluate creditworthiness of a borrower based on the type of credit, past credit history, and expected ability to repay the loan in the future. Credit reports compile information on a person’s credit history, and lenders use credit scores to assess a potential borrower’s creditworthiness. A low credit score can result in a lender denying credit to someone they perceive as having a low level of creditworthiness. Common types of credit include credit cards, auto loans, home mortgage loans, and student loans. The cost of post-secondary education can be financed through a combination of grants, scholarships, work-study, savings, and federal or private student loans.
Standard: 3
- Students will understand that: People who have sufficient income can choose to save some of it for future uses such as emergencies or later purchases. Savings decisions depend on individual preferences and circumstances. Funds needed for transactions, bill-paying, or purchases, are commonly held in federally insured checking or savings accounts at financial institutions because these accounts offer easy access to their money and low risk. Interest rates, fees, and other account features vary by type of account and between financial institutions, with higher rates resulting in greater compound interest earned by savers.
Standard: 2
- Students will understand that: A budget is a plan for allocating a person’s spendable income to necessary and desired goods and services. When there is sufficient money in their budget, people may decide to give money to others, save, or invest to achieve future goals. People can often improve their financial wellbeing by making well-informed spending decisions, which includes critical evaluation of price, quality, product information, and method of payment. Individual spending decisions may be influenced by financial constraints, personal preferences, unique needs, peers, and advertising.
In this math lesson, students will examine and calculate interest on loans and investments.
Resources
Procedure
This lesson is presented by Council for Economic Education in partnership with FiCycle.
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.)