The students will see how compounding returns make investing at a young age pay off.

### STUDENTS WILL

• Explore the relationship between the opportunity cost of investing and the time value of money with compounding interest.
• Calculate the potential accumulation of wealth for investors who begin saving at different ages.

### INTRODUCTION

Allocating resources between consumption today and investment for tomorrow is one of the critical choices all citizens are faced with. As retirement funding in the United States becomes more focused on individual savings rather than corporate pensions and government programs, it becomes more important for all students to understand this tradeoff. This lesson is designed to give the students a better understanding of compounding returns on an investment. The lesson also can be a powerful tool to use in determining the opportunity costs of consumption versus investment decisions.

### PROCESS

Questions for Thought:

1. If person A saves \$24,000 for retirement and person B saves \$72,000 toward retirement, and they both earn the same rate of return, which one will have more money at retirement? [Person B.]

2. Suppose person A and person B both invest \$24,000, but person A invests it at age 25 and person B invests it at age 55. Again, if they both earn the same rate of return, who will have more money at age 65? [The students should recognize that person A will have more money. If they don't see this, it may be a good idea to review compound versus simple interest before going any further.]

Let's look at a couple of hypothetical investors and see how the choice of when to invest affects the amount of money available at retirement.

Our investors are two 23-year-old women who have just graduated from college and started their careers. For the first two years after college neither woman saves any money toward retirement; both focus instead on establishing their careers and purchasing household items. At age 25, Mia Saver starts to save money for retirement by investing \$200 per month into an account paying 7% annual interest compounded annually. Ima Spender continues to spend all of her money. From ages 25 to 35, Ima drives a nicer car than Mia and takes a more elaborate vacation each year.

When the women reach age 35, Mia Saver chooses to work only part time, so she does not invest any more money into her retirement fund. However, she leaves it invested in the account paying 7% annually. At age 35, Ima Spender begins investing \$200 per month toward retirement. Ima's account also pays a 7% rate of return compounded annually. Ima invests \$200 per month for 30 years, until age 65.

[Note: Click on the Compounding Interest Graphing Tool: it will give the students a visual representation of how quickly compound interest can build.]

Have the students use the Savings Calculator website to complete the Worksheet showing the value of the accounts every 10 years. You may need to do the first couple of calculations as a class to make sure the students understand the calculator.

After everyone has completed the top half of the spreadsheet, compare the answers. [At a 7% rate of return, Mia Saver, who only invested \$24,000, but invested it early, has \$261,893 for retirement. Ima Spender, who invested \$72,000 over 30 years has less: \$235,215.]

The students should repeat the exercise using another rate of return

(8% recommended)

on the lower half of the worksheet to confirm the results. Another option is to let the students choose their own rates of return, within a reasonable range, and compare their results with those of other classmates.

Attached is a Key with the worksheet completed, using a 7% rate of return on the top half and an 8% rate on the lower half.

### ASSESSMENT ACTIVITY

Have the students turn in their completed spreadsheet and a short paragraph summarizing the power of compound interest.

### CONCLUSION

Due to the power of compounding returns, a small investment made early in life can lead to a larger account balance than a larger investment made later in life.

### EXTENSION ACTIVITY

1. Integrate lesson concepts with mathematics. Help the students derive the formulas for calculating compound interest. The financial calculator website has options for compounding interest daily, monthly, quarterly, or annually. You can compare the differences between compounding formulas and earnings potential. Also, the students can use algebra to solve the interest formulas for the exact rate of return Ima Spender would need to earn in order to catch up to Mia Saver's account balance by retirement.

2. Make use of investment concepts. Have the students find the rate of return Ima Spender would have to earn in order to catch up to the account balance of Mia Saver by retirement. [If Mia earns 7%, Ima would have to earn 7.57%; if Mia earns 8%, Ima would have to earn 9.32%.] You can compare these results to different rates of return on different investments and discuss the risk/return tradeoff investors have to make. (Keep watching EconEdLink: I hope to have a lesson covering investment characteristics there soon.)

3. Integrate lesson concepts with history. Have the students look up the rate of return on different investments for the past 75 years, or during the decade you are currently studying. Some useful web-sites to consult are the following:

## EDUCATOR REVIEWS

• “This is superb! The cases set up the miracle of compound interest. The calculators allow kids to play with -- and therefor reinforce -- the concept. My students loved this. I'm using it as a pre-teaching lesson before we learn about stock market investing. It beautifully answers the questions "Why should I invest?" and "Why should I start now?" My kids are interested in investing. I'm trying to use that interest to drive them back to the necessity of understanding economic fundamentals.”

Mike A., Fort Worth, TX   POSTED ON March 20, 2013