I was re-watching classic Futurama while trying to relax before a night shift when Disney+ offered me this episode:
Now I’m a big fan of the power of compound interest, and often chat to colleagues about investments and making money work for you… but even to me, that number seems surprisingly large. But it’s Futurama, so of course they did the maths.
Compounding in this sense means that every time you earn interest on that money, you reinvest that interest so you then earn interest on that slightly bigger amount next year. So in this case, with a principle investment
So why is this number so surprising? The problem is that compounding is an exponential phenomena, and we’re really bad at it.
It makes sense. As a species we’re masters of many things, but understanding exponential growth isn’t one of them. Our brains have been honed by eons of evolution and millenia of society to live in a largely linear world, so we’re basically hardwired to see everything as straight lines rather than hockey stick curves.
When you think about it, almost all human experiences are linear. If you walk for an hour, you cover roughly twice the distance you would in half an hour. If you plant ten seeds, you expected roughly ten times the harvest of a single seed. Our intuition, therefore, developed to predict and interpret these direct, additive relationships. We have evolved to think in terms of cause and effect where a proportional input yields a proportional output.
This linear intuition served us well in a world where resources, threats, and even social interactions often scaled in a relatively predictable, additive manner.The problem arises when we confront exponential phenomena. Here, the growth isn’t additive; it’s multiplicative. A quantity doesn’t just increase by a fixed amount, rather it increases by a fixed percentage of its current value. This evolutionary predisposition is further compounded by societal factors. Our education systems, while teaching the mathematics of exponents, often fail to instill an intuitive understanding of their real-world implications. News reporting frequently presents data in linear terms, obscuring the exponential nature of many trends. Even our language subtly reinforces linear thinking, with phrases like “a steady increase” often masking the potential for rapid, exponential acceleration.
Exponential growth and disease
Although helpful in everyday life, when it comes to big issues like health and finance, this is a risky way of thinking. Consider the COVID-19 pandemic as a stark example. In the early days, the number of cases was doubling every few days. From a linear perspective, going from 100 cases to 200 cases might not seem alarming. However, that same doubling pattern quickly leads to 400, 800, 1600, and so on, transforming a seemingly small initial number into a massive outbreak in a matter of weeks. The failure to grasp this exponential growth early on led to delayed responses in many parts of the world, with devastating consequences. The initial, seemingly small numbers lulled people into a false sense of security.
Compound interest
However, this is precisely where the power of compound interest lies, and where our linear bias can cost us dearly. Compound interest means earning returns not just on your initial investment, but also on the accumulated interest from previous periods. It’s interest earning interest, creating a snowball effect that grows larger and faster over time.
I use my own example of failing to figure this out when encouraging others to save. In the UK we have a product called the Lifetime ISA, which allows individuals to save up to £4k a year, and the government top that up by 25% to a maximum of £5k. Other ISA and savings products are available, but for the sake of keeping the maths straightforward lets stick to the LISA.
If I’d have started saving in my LISA when I first left full-time education, assuming a modest return on stocks and shares of around ~7%, my savings will hopefully be looking something like this as I approach retirement:
Sadly, the import word there is if. Instead I frittered a lot of money away on cars, wine, and holidays, and only really took investing seriously when I got my registrar training number, meaning it will probably look closer to this:
The me who’ll have invested for 30 years will have saved £150,000 over that time, but due to the power of compounding it’ll be worth a phenomenal five times that at £505,365. However, the me who’d have started just 10 years earlier would have double that at £1,068,047, despite it only costing £50,000 more in investments. The difference of just ten years at the beginning – a seemingly small delay from a linear perspective – results in a massive discrepancy in the final accumulated wealth.
This is because starting earlier would have allowed my money to compound for an extra decade, a period during which the growth was less noticeable initially but became exponentially powerful towards the later years. On the other hand, I missed out on those crucial early compounding years when the foundation for explosive growth is laid, and mostly wasted this on depreciating assets instead.
However, this isn’t about a woe is me post, or even blaming ourselves for a naturally evolved cognitive bias. It’s about recognising that it exists, and actively working to counteract it. Understanding that compound interest is an exponential phenomenon, not a linear one, is a crucial first step in this. Obviously, the second is then to act on that understanding by starting to invest as early as possible, even if the initial amounts seem small. Because when it comes to your financial future, the biggest loss isn’t always the one you incur, but the gain you never made due to the silent, invisible power of exponential growth working against you.
I feel obliged here to point out that I am not a financial adviser, and that the content of this post is for informational and educational purposes only and should not be considered financial advice. Investing involves risk, and the value of investments can go down as well as up. Nothing I’ve said here takes into account your individual financial situation, risk tolerance, or investment objectives. Before making any financial decisions, I strongly recommend consulting with a qualified and regulated financial professional. Medics Money have a great service matching health professionals to IFAs which I’ve personally found really useful.
Compound debt
It’s also important to remember that the exponential sword cuts both ways. While compound interest can be your greatest ally, compound debt can be your most formidable foe.
Nowhere is this more apparent than with credit cards. Many people, again falling victim to linear thinking, see a minimum payment as a manageable linear expense, failing to grasp that the interest on credit card debt compounds rapidly, often at rates of 20% or more annually. This way a small balance can quickly balloon into an unmanageable sum, with the majority of your payments going towards servicing the interest rather than reducing the overall amount you owe. This creates a vicious cycle that traps people in debt, as the exponential growth of their debt outpaces their ability to pay it down.
Mortgages, while generally carrying much lower interest rates than credit cards, also demonstrate the power of exponential mathematics over time. When you take out a 25 or 30-year mortgage, the initial years are heavily weighted towards interest payments. Many homeowners are surprised to learn how little of their early repayments actually go towards reducing the principal amount of their loan. This is because the interest is calculated on the remaining, much larger, principal balance. Overpaying your mortgage, even by a small amount each month, can dramatically reduce the total interest paid and shorten the loan term, precisely because you are attacking the principal earlier, allowing less time for interest to compound against you.
Given these dynamics, a common question is should you prioritise investing or overpaying your mortgage? There’s no one-size-fits-all answer, as it depends on individual circumstances, risk tolerance, and the prevailing interest rates. Generally, the decision hinges on comparing the interest rate on your mortgage with the expected return on your investments, and whether you’re planning on moving soon (and hence reducing your LTV might be beneficial) vs staying in one place. Again, speak to a financial adviser!
Ultimately, the key mitigation strategy against our linear bias in all aspects of life - be this personal finance or avoiding the winter ’flu - is awareness. Understand that bad things like debt and pathogens grow exponentially, but also recognise that we can make it work for us too by allowing investments to grow exponentially over time. Keeping the long-term, exponential perspective in mind allows you to harness the power of exponential growth to your advantage, rather than letting it silently erode your financial well-being.
But the chance of ending up in a cryochamber and benefiting from a millennium of compound interest remains very slim for all of us.