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Lesson

# Compound Interest

Updated: July 15 2019,
Author: Sharra Jones

### Concepts

Students learn what compound interest is, how it is calculated, and appreciate the impact it makes on loans and investments. To begin the lesson students work through simple interest leading to compound interest problems. The students find the balance over time using compound interest as well as determine how much interest will be paid over a period of time.

90 minutes

### Will Be Able To

• Define saving, principal, interest, interest rate, simple interest and compound interest.
• Explain the factors that affect the amount of compound interest earned or paid.
• Explain why banks pay interest and why creditors charge interest.
• Calculate simple and compound interest.
• Calculate the total amount of a loan or total amount of a set amount of savings over various time periods.
• Explain how compound interest can help and hurt you.

### Procedure

1. Display Slide 1. Ask students what they think compound interest is. (Accept all answers. Do not give them a definition at this time.) Tell them that this lesson is about compound interest and how it can help and hurt you.
2. Display Slide 2. Ask students to read the information on the slide. Explain that saving is disposable income (income after taxes) minus consumption spending (money spent on goods and services). Point out that, just like Desmond, people save to be able to buy things in the future. Discuss:
1. What does Desmond want to buy in the future? [Car.]
2. Which option should Desmond choose and why? [Desmond should choose option B. He could earn \$100 every Saturday mowing lawns. However, because of the service fee he will only have \$75 to save. It will take over 33 Saturdays to earn \$2500.  If he works for his dad, he will have to work 20 Saturdays to save the money because his dad will not only pay him for his work but contribute \$25 to Desmond’s savings for every \$100 Desmond saves.]
3. Display Slide 3 and review. Tell students that interest is the amount of money that people pay to borrow money or the amount of money that people earn when they save money. Explain that to calculate simple interest we use the formula I=Prt where I is the interest earned, P is the principal (the principal is the original amount of money deposited minus interest or the original amount of a loan without any interest), r is the annual interest rate (the percentage of the amount of a loan that is charged for a loan; also, the percentage paid on a savings account) as a decimal, and t is the time in years.
4. Display Slide 4. Pose the following problem: Dianna deposits \$725 into a savings account that pays 2.3% simple annual interest. How much interest will Dianna earn after 18 months?
5. Display Slide 5. Explain that simple interest is interest paid only on the original principal. Point out that the problem is to determine how much interest Dianna will earn on her initial deposit after 18 months. Tell students that 18 months is written as 1.5 years and the interest rate is 2.3% which is written as 0.023. Walk the students through the formula for simple interest to solve the problem. [\$25.01]
6. Display Slide 6. Ask students to solve the problem using the simple interest formula. Discuss the answers as a class.
1. What number did you use for p? [\$550, \$870]
2. What number did you use for r? [0.07, 0.037]
3. What number did you use for t? [4, 2.5]
4. Did you have to change “t” to years? [No, it was already years. Yes, time was 30 months which equals 2.5 years.]
5. How much interest was earned? [\$154, \$80.48]
7. Display Slide 7. Explain that compound interest is interest that is earned on both the principal and any interest that has been earned previously. Give some examples of how compound interest affects people. Compound interest is earned on many savings account deposits at banks and credit unions; compound interest is earned on annuities, which are insurance products; compound interest is paid on unpaid credit card balances, on car loans, and on mortgages.
8. Explain that interest can be compounded over different lengths of time. Compounded annually means that interest is computed and added at the end of each year. Compounded semi-annually (twice a year) means that interest is computed and added every six months. Compounded quarterly (four times a year) means that at the end of each quarter (three months) interest is computed and added. Compounded monthly means that interest is computed and added at the end of each month.
9. Tell students that they are going to watch a video and ask them to listen for how people can make their money grow. Show the video using the following link: https://www.stlouisfed.org/education/no-frills-money-skills-video-series/episode-1-growing-money-compound-interest . When the video is finished, discuss the following:
1. What organization insures the money in people’s bank accounts? [Federal Deposit Insurance Corporation.]
2. What is the best plan for building your saving? [Pay yourself first.]
3. What do we call the price people pay for using someone else’s money? [Interest.]
4. What is the amount of money initially deposited into a bank account that pays interest called? [Principal.]
5. Why do you think banks pay interest? [Because they use the deposits to make loans to other customers. They are paying interest as the price for using customers’ money.]
6. When was the young woman in the video better off — when she started saving early or when she waited to save? [When she started saving early.]
7. When did she earn more interest? [When she was able to receive a higher interest rate.]
8. How did saving regularly benefit her? [By saving regularly she had more money in her account on which to earn interest.]
10. Display Slide 8. Explain the compound interest formula. Compound interest formula: where A represents the amount of money in the account at the end of the time period, P is the principal, r is the annual interest rate, and t is the time in years.Display Slide 9. Pose the problem (Simon deposits \$400 in an account that pays 3% interest compounded annually).
11. Ask students what the balance is in Simon’s account at the end of two years. Explain that the first step is to find the balance at the end of the first year using the simple interest formula I=Prt, which is \$12. Remind students that they must change the interest rate into a decimal and time into years. Then add the interest to the principal balance, which makes the answer \$412.0
12. Explain that the next step is to find the interest at the end of the second year using the simple interest formula and the principal of \$412. The interest at the end of the second year is \$12.36. The final step is to add \$412 to \$12.36 to get the account balance at the end of two years which is \$424.36. Ask the students how much more interest was earned as a result of compounding than had the account earned only simple interest. [\$.36] Point out that this doesn’t seem like much, but as they saw in the video, over time it adds up.
13. Display Slide 10. Now have the students try the following problem and discuss the answers as a class:
• Principal: \$600, Annual rate: 4%, Time: 3 years
• Balance at the end of the first year is ________. [\$624.00]
• Balance at the end of the second year is ________. [\$648.96]
• Balance at the end of the third year is ________. [\$674.92]
14. Ask the students how much more interest was earned through compounding than would have been earned with only simple interest. [\$74.92-\$72 = \$2.92]
15. Display Slide 11. Pose the following problem: Jackie deposits \$325 in an account that pays 4.1% interest compounded annually.
16. Ask students how much money Jackie will have in her account after three years. Explain to the students that in this example they will use the compound interest formula. They should use \$325 for p, change 4.1% into 0.041 and use that number for r, and since 3 is already in years, use that for t. Ask students to complete the calculation. [\$366.64]
17. Display Slide 12. Ask student to solve the problems using the compound interest formula.
18. Discuss the following.
1. What numbers did you use for p, r, and t? [p=285, r= 0.019, t=6]
2. Did you have to change the time into years and if so, to what did you change it? [no]
3. What was the interest rate? [\$319.07]
4. Repeat the same questions for the second problem. [p=1200, r=0.087, t=2, no]
5. What was the account balance at the end of time period specified for each account? [\$1417.88]
19. Display Slide 13. Use the interest calculator found at http://technology.councilforeconed.org/interest-calculator/ to redo the compound interest problems above. Change the year or the annual rate and show the students how the amount changes. Manipulate any of the variables to give the students an idea of how compound interest works.
20. Display Slides 14-19. Stress the importance of investing money over time and how the longer the term the greater the rewards. Work through examples together using the calculator. Discuss interest that compounds more than once per year. Point out that the more often interest is compounded the greater the return. Provide the revised formula. Work through a few examples. Demonstrate the effect of compounding periods over long term investments or loans using the calculator.
21. Display Slide 20. Have the students work through the two problems and determine which is the better choice. [1. \$1343.92, 2. \$33,911.46, number 2 is the better choice.]

### Assessment Activity

1. Which of the following affect how much earnings people will receive on a deposit in a savings account?
1. [How long they save, how often they make additional deposits, what the interest rate is, how often interest is compounded.]
2. How long they save, how old they are, what the interest rate is, how often interest is compounded.
3. How long they save, how often they make additional deposits, what the interest rate is, what their income is.
4. How long they save, how old they are, what the interest rate is, how often interest is compounded, what their income is.
2. Xavier has a savings account. The interest that is earned on both the principal and any interest that has been earned previously is an example of _______________.
1. Risk
2. Simple interest
3. Interest rates
4. [Compound interest]
3. The first credit card that you got charges 12.49% interest to its customers and compounds that interest monthly. Within one day of getting your first credit card, you max out the credit limit by spending \$1,200.00. If you do not buy anything else on the card and you do not make any payments, how much money would you owe the company after 6 months?
1. [\$1276.92]
2. \$76.92
3. \$12.49
4. \$1212.49
4. You win the lottery and get \$1,000,000. You decide that you want to invest all of the money in a savings account. However, your bank has two different plans. Five years from now, which plan will provide you with more money? Show your work.
1. The bank gives you a 6% interest rate and compounds the interest each month.
2. [The bank gives you a 12% interest rate and compounds the interest every 2 months.]

### Conclusion

1. Tell students that they are going to do an activity that makes what they have been learning relevant to real life. Distribute a copy of Activity 1 to each student. After students have completed the worksheet, review their answers using the Activity 1: Answer Key.
2. Discuss the following:
1. What is saving? [Saving is disposable income (income after taxes) minus consumption spending (money spent on goods and services).]
2. Why do people save? [To buy goods and services in the future.]
3. What is principal? [The original amount of money deposited minus interest or the original amount of a loan without any interest.]
4. What is interest rate? [The percentage of the amount of a loan that is charged for a loan. Also, the percentage paid on a savings account.]
5. What is interest? [The amount of money that people pay to borrow money or the amount of money that people earn when they save money.]
6. Why do banks pay interest? [They use customer deposits, which may represent savers, to make loans to other customers, who are borrowers.]
7. What is simple interest? [Interest paid only on the principal.]
8. What is compound interest? [Interest paid on the principal and on any interest earned.]
9. What factors affect how much interest someone earns on their deposits? [For example, how long they save, how regularly they save, how much interest is paid, how often the interest is compounded.]
10. How does compound interest affect the use of credit cards? [If balances aren’t paid in full each month, the account holder is charged interest on the original balance as well as any interest charged.]
3. Explain how time affects the amount of compound interest earned or paid. [The more often the interest is compounded on interest earned, the more money you are paid to save. The more often the interest is compounded on interest paid on a loan, the more money that is being paid to creditors.]
4. Explain why banks pay interest and why creditors charge interest. [Banks pay interest for using the customers’ deposits to make loans; whereas creditors charge interest for loaning you the money.]

### Overview

Compound interest is a way of life in our society. Understanding how it works and how it can be used effectively to grow your investments is a critical lesson. Investing early and accumulating compound interest over the long term is an excellent way to make your money work for you. Interest can also work against you. For example, credit card companies charge interest every month on the balance owed; if you make only a minimal payment each month you will have to repay more than you spent on purchases.