Understanding Compounding – Part One

Introduction

Einstein described compound interest as: “the eighth wonder of the world. He who understands it, earns it… he who doesn’t, pays it.”

Compounding is perhaps the ultimate financial first principle. It underpins all discussion about building wealth and does so from two angles, just like Einstein said. I mean, who am I to dispute the genius of Einstein?!

You’ll also see me refer to ‘yield’ in this post. Yield is usually expressed as a percentage. So, if you have a share worth £100 that produces a dividend of £4, that’s a 4% yield. Here, I’m simply using it to refer to the income produced by investments, as opposed to the growth in the value of those investments due to market movements.

Everything You Need to KNOW

What is Compounding?

Compounding is easiest to explain by thinking in terms of interest on a bank deposit. Let’s say you have £100 in the bank, and you get 4% interest. At the end of year one, you will end up with £104. At the end of year two you will have earned interest on top of year one’s interest. So now you have £108.16.

At the end of year three, you have £112.49. It would take 18 years to double your money and 38 years to quadruple it. The rate of increase starts slow and builds picks up the pace over time.

Compounding gets more interesting when applied to real assets like shares, because now the interest you are earning buys you more shares, which themselves both rise in value (hopefully) and produce income of their own.

Compounding then, is the prices of using money to buy more stuff that generates you more money. As the numbers get larger, and the number of iterations increases, the bigger the impact.

2. Compounding Works for You

Inflation works in your favour. Let’s take the compound interest example and apply it to real assets like shares. In this example, the shares you buy have an income yield of 4% and they grow in value by 5% per year – not too shabby.

Imagine you have 100 shares worth £1 each. In year one you make £4 of income and by the end of the year each share is worth £1.05. You use the £4 income to buy more shares at the new price of £1.05, so you now have 103.81 shares worth £1.05 each, so you have £109 of shares.

Each year, you buy more shares with the income, and the value of each share you own increase by 5%. Bear in mind you haven’t put any more money in, you’re just using the income to buy more shares and getting the growth on more shares each year as a result.

At this rate you would double your money to £200 in ten years, but it would only take just under another six years to triple it to over £300. You wold quadruple your money in 20 years, and you would 10x your money in just over 35 years. Compare that to the compound interest, where the interest rolls up but there’s no asset with a price to go up, your money would double in just under 19 years with a 4% interest rate.

3. Compounding can Work Against You

Now let’s say that you hold those shares in a fund where the costs are 1.5% per year. We’ll take that off the yield for the purposes of this, so now you only have a 2.5% yield with which to buy more units each year.

It will take you 12 years to double your money and 26 to quadruple it. In 35 years, rather than having 10x the money, over £1,000, you would have £636. That’s not bad, but those costs have wiped out over a third of your final pot. This is because what you spend on costs is making someone else rich.

There are some who say that costs are irrelevant if the fund you choose has great performance, and that by concentrating on costs, you’re focused on stuff that doesn’t really matter.

For example, if you have costs of 1.5% taken off the yield but you get another 2% of growth you’d have a 7% annual growth in all. You would still double your money in 10 years, but it would take you 22 years, not 20 to quadruple it, and 41.5 years, not 35 to 10x your money.

If you take costs off the growth rate rather than the yield, you’re slightly better off. It would still take you 12 years to double your money, but would take you 23 years, not 26 to quadruple it and 39 years, not 48 to 10x your money. Here’s a spreadsheet which shows how it works.

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* This article was originally published here