# Lesson 2: Analyzing Change/Growth and Decay Formula

In this lesson, students will be able to identify what interest is as it pertains to saving and investing, as well as calculate simple and compound interest.

**OBJECTIVE**

Students will be able to identify what interest is as it pertains to saving and investing; calculate simple and compound interest; apply the compound interest formula (i.e., the growth and decay formula) to nonfinancial situations.

**MATERIALS**

- Ads from financial institutions indicating interest rates paid on savings and investment accounts
- Student calculators (for Worksheet 2; can also be done without calculators)
- Worksheet 2 (PDF) — Content Connections: Percentages, Exponents
- Bonus Worksheet 2 (PDF) — Content Connections: Conversion of Percentages to Decimals, Exponents
- Take-Home Activity 2 (PDF) — Content Connections: Percentages, Exponents
- Resource: Answer Key (PDF)
- Resource: Mini-Poster (PDF)

Click for *whiteboard-ready printables.*

**DIRECTIONS**

**Time required:** 20-30 minutes, depending on class review needs; additional time for worksheets

Getting Started

1. Show a savings or investment ad to the class. Ask students to explain what the interest rate (e.g., 1.75%) means. Establish that the interest rate represents the rate of payment by the financial institution to the depositor in return for depositing money with the institution.

2. Using the example of a $1,000 CD deposited for one year with a 2% interest rate, show the calculation $1,000 · .02 · 1 = $20. Work the calculation as necessary and generalize the formula by writing the following formula for simple interest: *I* = *p* · *r *· *t*, where *I *= interest, *p *= principal (amount deposited), *r *= rate (of interest), and *t* = time (in years). It might also be useful to show the class that the total value of the CD at maturity equals Principal + Interest (Principal · Rate · Time). If necessary, explain to the class that the interest rate is in effect the entire term of the CD. (If a student asks, it may be necessary to explain that interest also comes into play when a financial institution loans money. In these cases, the borrower pays interest to the financial institution.)

3. Ask students what they think would happen if the bank offered a two-year CD. Because this is a case of simple interest, indicate that the bank will pay the interest at the end of each year. This results in a $20 payment at the end of each year. Plug these numbers into the formula *I* = *p* · *r* · *t* to show how a total of $40 in interest will be paid. To show how much the depositor has in total, show how to add the interest to the principal, i.e., $1,000 + $40 = $1,040.

4. Ask what would happen if the depositor kept the first year's interest in the account to "grow." Show how the depositor would earn an extra 40¢ by using the $20 as principal for one year (the second year of the CD's term) at 2%. Explain that this is an example of compound interest.

5. Indicate that there is a formula that can be used to calculate how money grows with compound interest:* y* = *a*(1+*r*)*n* where *y* = ending value, *a* = starting amount (in this case principal or amount invested), *r* = interest rate, and n = the number of time periods. The amount of interest can be determined by subtracting the starting principal amount from the ending principal amount. Demonstrate with calculations from the two-year CD.

6. Distribute Worksheet 2: A Case of Interest (PDF) and classroom calculators. Read the introduction with the class and review the key facts before students complete the worksheet. Review answers as a class. Worksheets Answer Key (PDF)

7. Students will build on these skills in Bonus Worksheet 2: The Case of the Smelly Sandwich (PDF) and Take-Home Activity 2: The Case of the Decaying Car (PDF). If students require additional support, review worksheets as a class. Worksheets Answer Key (PDF)