Albert Einstein called compound interest the eighth wonder of the world. We want to teach students the value of investing early and steadily for their future. In our Foundations in Personal Finance: High School Edition chapter 3 we go over the story of Jack and Blake and the power of compound growth. Many interested students will search online for investment calculators and "crunch the numbers" to see if Jack really was able to make his early contributions grow to more than a million more than Blake while putting in way less money. Maybe you have too. Do your numbers match the numbers in the graph? Maybe, or maybe not. There are a lot of little factors that make a difference in the calculations, including the frequency of compounding. In our example, we use daily compounding which most accurately reflects what would happen with real investments.
When discussing this with your students, first, let's remember the power of compound growth in examples like this are just that: examples. Real world results will vary. Let's walk through how we came up with our final numbers (and you can too!) In our example we use the S&P average of "around 11 percent."
For Jack, we have to do two calculations. The compounding of his investment for the first nine years while he is contributing and a second calculation for the 38 years it grows with that starting balance. We know that Jack starts investing when he is 21 and invests $200 for a total of $21,600 for 108 months (9 years x 12 months = 108 months). Using our Ramsey Compound Intest Calculator we put in a $0 starting balance, contributing $200 a month for 9 years, at 11% interest, compounding daily, we get a result of $36,736. That becomes our starting balance for the next calculation.
Here's where it gets tricky, and your calculations might be off a little. We say that Blake starts investing and Jack stops when they are both 30. They compare their final values when they are 67. So that's 38 years of growth. But how far into their 67th year do they stop to compare? You see where it gets tricky. If you just punch in 38 years in your investment calculator, you should get a result of around $2.399 million for Jack. If you put in 39 years, you should get a result of $2.679 million. One number is a little under and one is a little over the graph in the curriculum. So, the actual time would be more accurately calculated at about 38 and a half years.
Again, this is just an example. Whether you use 38 years, 39 years, daily compounding, or annual compounding in your calculations, Blake never catches up. That's the lesson we want students to learn.
Start early and invest consistently over time to capture the power of compound growth.
Want to do it by hand, remember the formula from your text:
We hope this helps you in your classroom discussions.