The Myth of Ben and Arthur

I’m currently reading Dave Ramsey’s book The Complete Guide to Money. So far I’ve read about 20% of the book and I’m enjoying it. It’s certainly a good read on personal finance and includes some great ideas for sorting out your finances. However, I came across the story of Ben and Arthur. This is a popular story about the importance of saving early for retirement and the power of compounding your returns.

The Story

The story involves two characters, Ben and Arthur, who are the same age. Ben begins saving $2,000 a year into his retirement account at the age of 18. He continues to add an additional $2,000 every year for the next 7 years until he is 25 years old. Then he stops saving completely and just leave the money in the account to grow. His total contributions amount to $16,000.

Arthur on the other hand puts off opening a retirement account until he is 25 (the same age that Ben stops saving). At 25 he puts $2,000 a year into the account. He does this every year until he is ready to retire when he is 65 years old. So Arthur saves for a total of 40 years and contributes a total of $80,000 into his pension pot.

Financial Trickery

Now comes the financial trickery. For some reason, he doesn’t explain why, Dave Ramsey assigns a 12% growth rate to the funds each year. At this growth rate Ben ends up with a $2,288,996 pension pot on his 65th birthday (remember he only contributed $16,000) and Arthur ends up with $1,532,166. Arthur is about $750,000 worse off than Ben because he started saving early. So the lesson here is to start saving as early as you can which of course is good advice.

The problem I have is the 12% growth rate. Remember this is the net growth rate too, after any fees on the retirement fund. If we change that 12% to a more realistic 7% a year we end up with the following scenario: Ben, who presumably spends 40 years of his life partying because he has saved for 8 years early, ends up with $307,270 and Arthur ends up with $399,270. This time Arthur has beaten Ben although both have much smaller pension pots. They are no longer millionaires who can enjoy their retirement. Using the 4% rule Ben’s retirement income would be around $12,000 a year (compared to over $90,000 a year with the 12% growth rate) and Arthur will get just under $16,000 a year instead of over $60,000 with the 12% growth rate. And these figures don’t even take into account 40+ years of inflation.

Clearly the projected growth rate you place on your savings makes a huge difference to the outcomes. I would say that both Ben and Arthur need to save more, and Ben cannot stop saving after 8 years. Being over optimistic in your growth estimates can lead you to under-save for retirement. For example if you believed you could make 20% a year on your investments then having $1,000 invested when you are 25 could compound to $1.5m by the time you are 65. You might be fooled into thinking you don’t need to save any more money and can simply enjoy your full paycheck each month.

There are clearly dangers of using compounding for projections. Even small changes to a growth rate can make big differences to final outcomes, especially when looking over long time frames. For example $1,000 invested at 7% a year for 40 years becomes around $15,000. Invested at 6% for 40 years it becomes around $10,000. That 1% point results in a 50% difference to the final outcome.

Is 12% too high?

So where did Dave Ramsey get that 12% a year growth rate from? In today’s markets 12% might sound reasonable. In the last 8 years the S&P500 has compounded at 17% annually. However we are in one of the biggest bull markets in history. In the 8 years prior to that (2001 to 2009) the S&P500 compounded a negative 7.5% annually. Looking back over a longer time frame the 20 year returns on the S&P500 (excluding dividends) amounts to just under 5% a year. I’m guessing closer to 7% with dividends. And that’s for the S&P500, if you live in the UK then the story of the FTSE100 is even worse. The 20 year return on the FTSE is just over 2%. Dividends tend to be higher in the UK but I can’t see that figure being much above 5%.

End note

Be cautious when you see projections using grand growth rates in the 8-12% range. I tend to use 6-7% in my long term projections. Over the last 6 years, including lots of mistakes, I’ve averaged 7.7%. It’s better to err on the side of caution and over save than try to play catch up later on in your journey because you have been over optimistic with your forecasts.