Preamble: this is still one of my favourite posts. And a recent conversation about compound interest made me want to re-share it. Happy Friday.

There is an old article from 2010 that keeps making the rounds onto my facebook feed. It’s written by Dave at DaveRamsey.com, it’s called “How Teens Can Become Millionaires“, and the basic summary is this:

1. Ben invests \$2,000 per year between the ages of 19 and 26.
2. Arthur invests \$2,000 per year from the age of 27 until he retires at 65.
3. Both guys earn a 12% return on their money.
4. Ben has saved a total of \$16,000, while Arthur has saved a total of \$78,000.
5. But Ben is worth a lot more by the end.
6. This table:

Conclusion: don’t underestimate the power of compound interest, start early.

Some observations:

1. I agree, in principle, that we underestimate the power of compounding.
2. Except that I think this story is deeply deeply misleading. To the point where I feel a bit ill.
3. Mostly because it completely ignores some basic economics.
##### What happens when everyone earns compound interest?

So by far the biggest issue that I have is that Dave’s story implies that money somehow has its own value. As in: people can earn 12% per year, year on year, for years – but what you can buy with \$2,000 at age 19 is what you can buy with \$2,000 in 30 or 40 years’ time.

Um.

If everyone is earning that 12% return, then it means that people will have more money. But having more money does not mean that people will be wealthier – it more often means that prices will go up. So unless that return of 12% comes from real increases in productivity (like trees that make 12% more apples every year, or mines that produce 12% more gold every year – which is almost impossible over the period of time that we’re talking about), then prices will be going up at a similar rate.

So you can’t look at this as “money” alone. You have to look at this in terms of “purchasing power”. And I’m going to start by saying that, when Ben starts investing at age 19, the price of a nice meal for 2 people is around \$50. And that the price of the meal will keep up with your portfolio*.
*If you’re worried by this, don’t be. This assumption is about as crazy as the assumption that one could earn a 12% return indefinitely. But Dave set the parameters.

So let me re-do the graph for you, with some extra columns:

Based on this, we’re saying that Ben saves the equivalent of about 40 meals worth at the age of 19. Arthur, on the other hand, is barely missing a single meal per year from the age of 48 onwards.

The point is: if you’re going to glibly assume that there’s a 12% return available out there, then you can’t just “fix a savings amount” at \$2,000. You are no longer comparing the same things. And of course Ben is worth more at the end: in terms of real life sacrifice, he has forgone about 223 fun nights out, while Arthur has only missed out on 150 fine-dining experiences.

If you want to sort this out, you have to start by saying “both Ben and Arthur decide to pass on 40 restaurant dinners per year”. Then the graph looks like this:

Oh look! Arthur has saved more dinners-out. And he’s worth more. Well isn’t this less surprising.

So it looks like better determinants of future wealth are:

1. Knowing the difference between nominal and real returns (real returns are always “what can you buy with this?”, where nominal returns are “Oh look at these arbitrary money numbers”); and
2. A solid saving habit.
##### So where is the compound interest?

Well, there isn’t too much compound interest up top – because I’ve made the real return equal to zero. That is: the investment return of 12% is matching the increase in the price of meals (also going up at 12%).

In real life, some of the return will come from improvements in productivity (like people being able to communicate faster with faster internet speeds, etc). And it won’t all come through as increased prices – because greater productivity, in general, means that people are getting wealthier (because they can do more).

So let’s say that the price of meals is only going up at 9% per year, while both Ben and Arthur are still able to get their 12% return.

New graph:

Now we’re talking. Because even though it looks like Ben and Arthur have less in nominal terms (Arthur has saved \$8,073,475, as opposed to \$16,045,072); in real terms (ie. in terms of future dinners out), they’ve both saved more:

1. Arthur has enough for 3,065 dinners, instead of 1,747; and
2. Ben has enough for 1,139 dinners, instead of 358.

And that would be the power of compound interest: Arthur has less than doubled the purchasing power of his savings, while Ben has almost tripled his. Although Arthur has saved more, so he’ll still have more ‘savings’.

To Be Clear

That shift in purchasing power would be virtually the same if the inflation rate were 2% and the investment return 5%:

And I feel obligated to mention that. Because this “12% return” business is madness.

##### The key take-home messages
1. The earlier one starts saving, the better – agreed; but
2. Saving more means saving more; and
3. It’s not your bank balance that’s important, it’s what you can do with it.

Also – you haven’t missed out if you didn’t start early. The real benefit comes from the saving habit. And a saving habit that adjusts for inflation.

Rolling Alpha posts opinions on finance, economics, and the corporate life in general. Follow me on Twitter @RollingAlpha, and on Facebook at www.facebook.com/rollingalpha.