It's difficult to begin to write about compound interest without being tempted into hackneyed quotes from Albert Einstein. Since this article is only partially about compound interest, I shall resist with some enthusiasm. Even investment professionals, myself included, can lose sight of the power of compounding, and the impact that it can have over time is nothing short of staggering. Let me illustrate with an example which appears a little abstruse to begin with but the reasons for it will become clear as I move on to the main theme of the article.

Let's begin by going back to Ancient Egyptian times, say 2,000 BC. Imagine that we have a 1 metre cubed block. Now this block is added to each year and grows at a 2% rate. My question is how big will the block be today?

The size of London? The size of Europe? The size of the Earth? Your answer is way too small. Let's break down the problem down into bite sized chunks. Let us consider how many times larger will the block be after 100 years? At a 2% rate the block will double in size after 50 years and therefore be four times as large after 100 years in simple terms. However, this overlooks the effect of annual compounding. Once compounding gets to work, the block doubles every 33 years (or thereabouts), so after 100 years the block expands just shy of an impressive eightfold.

So, after 400 instances of expanding eight-fold, how big is our block? Roughly speaking it has grown to an impressive 2 x 10 34 metres in size. In fact, our metre cube has grown well outside of the solar system and way beyond Alpha Centauri, which at a 4 light year distance would have been swallowed up some time during the Dark Ages. This rather puts into perspective the impact of even modest growth rates over very long time periods.

This rather lumbering thought experiment brings me to the point of this article, what is the long term growth rate of the economy? Well, between 1830 and 2008 the UK economy grew by approximately 2% per year. This covered a period of massed industrialisation that lifted a large part of the population out of the fields, a slew of transformative technology such as electricity and the arrival of the car. It also incorporated a 2.5 times growth in population, lengthier working life times and the introduction of women into the workforce. It also admittedly included two devastating world wars, the 1930's depression and the 1970s inflation. Though surprisingly, these short term negative events have had little impact to the long-term health of the economy.

The Office of Budget Responsibility (OBR), which provides the Chancellor with economic forecasts, has a medium term growth expectation of 2%. This estimate, more or less, matches the economic growth rate since 1980. We know that economies cannot indefinitely grow at 2% rates and at some stage growth of this rate will become harder and harder to achieve, however, this may not happen in our lifetimes or even in our children's lifetimes.

However, I fear that growth in the UK economy may shortly be about to come under pressure for four main reasons. What we do know is that over recent years GDP has been swelled by population growth which has been running at a little over 0.5% pa thanks in large part to migration trends. It seems inevitable that Brexit will at least stall this. Secondly, in recent quarters, the economy has received a boost from falling savings rates. If we learnt anything from the credit crisis, we know that there is too much debt in the world and growth cannot be indefinitely brought forward through borrowing. Thirdly, we know that the baby boomers are beginning to retire and that dependency ratios are climbing. Fourthly, we are observing worrying trends in productivity which despite, or perhaps because of, new technologies that are changing the way in which we run our lives. What will the implications of Brexit on growth? So far the OBR has cut its growth forecasts by 2.4% over the next two years, further cuts may be forthcoming as the details of divorce become apparent.

What will be the implications of any growth shortfall? Clearly it will be very damaging to the government finances and will almost certainly require hikes in taxation. Incidentally, if the EU divorce bill is as much as £60bn, as some top end estimates place it, this is the equivalent of 40% of the government's annual income tax receipts. Higher taxes of course will slow the economy further. This cannot be good news for domestic company earnings but I see a real threat to the value of the pound. I stringently avoid making forecasts, especially about foreign exchange rates, but presently sterling appears as if it has all the lustre of a typical peso or lira currency.