Return

### INTRODUCTION

All of us make decisions continually about how to spend our limited amount of money (income) on goods and services that will make us feel satisfied and happy. But, of course, we also want to be capable of earning more money and consuming more goods tomorrow. In order to earn more money tomorrow, we have to use some of the income we earn today to invest in capital that will help us produce more tomorrow. How much would it take---in increased future earnings---to prompt you to reduce consumption today in order to free some money up for investment? Do you know what future consumption possibilities you might give up if you don't invest today--spending your entire income on consumption instead? After exploring the possibilities presented in this lesson, you will know.

You will calculate the total amount of money accumulated in an investment account in several different scenarios. By comparing the account values in different situations you will see how the length of time money is invested plays a large role in determining the ultimate value of the account.

### 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?

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?

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 of them 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 chooses to continue spending 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 she reaches age 65.

[Note: Before doing the following activity click on the Compounding Interest Graphing Tool; this will give you a better idea of how quickly your money can grow with compounding interest.]

Now go to the Savings Calculator . Use the calculator to complete the top half of the Worksheet showing how much money each woman will have in her investment account every 10 years from age 25 to 65.

Your teacher will give you instructions on what situation you should assume to complete the second half of the spreadsheet.

Now experiment with the calculator: Figure out what rate of return Ima Spender would have to earn on her investment in order to reach an account balance equal to Mia's balancer by age 65, if Mia's account earns 7%.

### CONCLUSION

Due to the power of compounding returns, a small investment made early in life can generate a larger amount than a larger investment made later in life. Investing for a longer time is more effective than waiting until you have a large amount to invest.

### ASSESSMENT ACTIVITY

Turn in your completed spreadsheet and a short paragraph summarizing the power of compound interest.

### EXTENSION ACTIVITY

1. See if you can derive the formula for calculating the account balance when interest is compounded over several time periods without any additional savings being added. Go back to the Savings Calculator to see if your formula is correct. For an extra challenge try to derive the formula to use when savings are added to the account each year.

2. Go to Yahoo! Finance page and download historical data on the S&P 500 or Dow Jones Industrial Average stock index. Use the index values to calculate the market rate of return at different times in history. You may also want to do the same thing with a stock you are interested in.
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