Here’s an infographic from moneyweb:

When I first looked this, I thought “Oh yes. Another ‘How Teens Can Become Millionaires‘ by saving just six annual deposits between the ages of 19 and 25…” And in case you haven’t read that, the spoiler alert is that I get very disparaging about the math.

The main problem in that post was this: most of us don’t know the difference between real returns and nominal returns. From what I can tell, we don’t even know that there is such a thing as a real return or a nominal return. We mostly just assume that interest is interest.

In reality though, there are two types of interest: real interest (actual return) and nominal interest (not-an-actual return).

“Nominal” interest pays no attention to what you can buy with your money – which makes it a bit meaningless, because the whole point of saving money is so that you can spend it one day in the future. But before you can even talk about ‘return’, you have to worry about inflation, which erodes it. So whenever we talk about earning returns, we’re actually conflating two goals:

1. Preserving purchasing power (ie. the return must first earn enough to cover any inflation); and then
2. Increasing capital (this is the real return).

If you’d like a formula:

or

Nominal Interest = Inflation + Real Interest

Fortunately, the above example from Sygnia actually takes both those factors into account.

That is:

1. Every year, the savings of Thandi and Harry are increased by inflation (most compound interest examples forget this!); and
2. The ultimate goal is treated as the same (saving R52 million by retirement age), so the final purchasing power goal is the same for both.

I think that this is a really clever way of showing the differences here. You don’t have to worry too much about who has more at the end (which is difficult to conceptualise, because inflation affects things) – all that you’re worrying about is the saving path.

Some graphs

Here are their annual savings contributions, adjusted by inflation:

So by not saving for 15 years, Harry has to forgo a lot more purchasing power than Thandi in order to reach the same investment goal.

If you want to look at this cumulatively:

I realise that that may look more convincing than the earlier graph: because Harry has to save a lot more capital than Thandi did in order to make up the interest differential.

Then overall:

Meaning that, if you take two people who want to reach the same investment goal, then it’s more painful to catch up if you start further down the line.

A Qualitative Caveat

Even though I’m a believer in compound interest, I do have a caution here.

Let’s say that Harry and Thandi are both going to start saving today. Harry is still 40, Thandi is still 25 – but they’re both aiming to achieve equivalent purchasing power saving points by their respective retirements at age 65.

In that case, what would Harry’s equivalent saving have to be in the same year that Thandi saves her first R30k? Well, at the existing ratio, Harry would have to save just over two and a half times as much as Thandi, making his first annual saving contribution around R80k.

On a monthly basis then:

• Thandi would have to save R2,500 per month; while
• Harry would have to save around R6,700 per month.

For the most part, salaries at age 25 are pretty low relative to salaries at age 40.

And because of that, it may well turn out that the higher purchasing power sacrifice is easier to swallow at age 40 than the smaller sacrifice at age 25 – because the disposable income of a 40 year old is so much greater than the disposable income of a 25 year old.

My main point is: purchasing power comparisons have to take into account one’s quality of life. If saving at a younger age means that you have to forgo some of life’s pleasures, while saving more at an older age means that you get to save while continuing to have fun, then it seems clear to this hedonist which option is the better lifestyle alternative.

Just a thought.

Rolling Alpha posts about finance, economics, and sometimes stuff that is only quite loosely related. Follow me on Twitter @RollingAlpha, or like my page on Facebook at www.facebook.com/rollingalpha. Or both.