Twins and investing

Suppose you have a twin. You start investing USD 10,000 annually for the next 10 years and then stop. At which point, your twin starts and also contributes USD 10,000 annually until retirement age. If no sales occur, who would have more money at age 65? How does the annual interest rate change the answer?

Assuming that the retirement age is far away, there will be an interest rate that creates a tie. With one higher, due to compounding interest, you will win because the more interest earns even more interest. With one lower, your twin will win because of more contribution total.

Suppose that you start contribution at age 30. As the chart shows, at 5.9% annual interest rate, there is a close tie at age 65. You would have contributed for 10 years, but your twin 25. Which person would you choose to be?

In this post, we will investigate if 5.9% annual interest rate is achievable for 35 years.

P.S. Here is the Jupyter notebook that generated the chart. It is parameterized so you can experiment with it.