Lesson 6  

Objectives: In this lesson, you will learn to calculate the return on investments for various rates and lengths. Also, you will compare results with the StocksQuest Calculator, which lists calculations year by year. Comparing the rates and lengths on investments, you will come away with a better understanding of how the power of compounding works.

Background: A simple way to calculate compounding is the rule of 72, which enables you to figure out how long it will take to double your money.  Take 72 divided by the rate of return, and you will get an idea of how many years before the initial investment will double.  For example, the usual return for the stock market is 12%.  Money would take 6 years to double because 72 / 12 = 6. Of course, the rule of 72 is just an approximation. You can use the actual formula to determine how long your money will take to double:

2P = P (1 + r / 100) k * n, where

P = principal
r = rate (usually an annual rate)
k = number of compounding times per year
n = number of years

Assuming a 10% rate of return, the equation would look like this:

2P = P (1 + 10 / 100) 1 * n

Then, cancel the P?s:
2 = (1 + 10 / 100) 1 * n

Next:
2 = 1.1n

Using natural logarithms from calculus, n is about 7.2725527, which is very close to the 7.2 using the rule of 72.

Activities:

  1. Assume John has earned $100 through a paper route. If he invests this money in a Standard & Poor's 500 (S&P 500) Index fund, which gives him a 12% rate of return annually, at the end of the first year, John will have:

Amount earned: $100 ´  0.12 = $12
Ending amount: $100 + $12 = $112

Here is what John will have in 6 years.

Year Beginning Amount ($) Rate of Return (%) Amount Earned ($) Ending Amount ($)
1 100.00 12 12.00 112.00
2 112.00 12 13.44 125.44
3 125.44 12 15.05 140.49
4 140.49 12 16.86 157.35
5 157.35 12 18.88 176.23
6 176.23 12 21.15 197.38

He will double his money.

  1. Complete the columns below:

How many years will it take John to double his money if he invests in a Treasury bond? ____ years

Year Beginning Amount ($) Rate of Return (%) Amount Earned ($) Ending Amount ($)
1 100 6 6 106
2        
3        
4        
5        
6        
7        
8        
9        
10        
11        
12        

Observe a pattern.

  1. From the previous example, you should predict the outcome of the columns below. How long will it take John to double his money?

Rate of Return (%) Number of Years
12 6
6 12
  3
24  
  18
10  
  9

  1. How accurate is the rule of 72? Complete the columns below with the help of the StocksQuest Calculator. Click here to use the Calculator. Like any general rule, the rule of 72 is just an approximation. For exact calculations, students can go directly to the Calculator section.

Rate of Return (%) Rule of 72 Actual
(from Calculator)
1 72.00  
2 36.08  
3 24.00  
4 18.00  
5 14.40  
6 12.00  
7 10.29  
8 9.00  
9 8.00  
10 7.20  
15 4.80  
20 3.60  
30 2.40  
40 1.80  
50 1.44  
100 0.72 1.00*

* 38% error

Additional Activities:

  1. The reverse of the rule of 72 can tell students how many years before their money is worth only half of its original value. Let's say inflation is at 4%  per year. A dollar today will be worth only $0.50 in 18 years since 72 / 4 = 18. How many years will it take to lose half of the purchasing power? Complete the columns below:

Inflation Rate (%) Number of Years
4 18
3  
  24
10  
5  
  7

  1. Lesson 13 "What is Your Future Worth?" explains more of the value of the power of compounding.

 

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