📚 Sunday evening read: Compounding your returns 💰

Read any article about compound interest and it’s likely to start with a reference to Einstein calling it the “Eighth wonder of the world”.

Like most pithy quotes from Einstein, he probably never said it. :sweat_smile:

Here’s a real quote from Einstein:

“In the temple of science are many mansions, and various indeed are they that dwell therein and the motives that have led them thither.”

So you can see why people make them up.

But compounding is pretty nifty, not to mention a vital part of investing. :ok_hand:

To understand it, first you need to get to grips with non-compound or simple interest.

Simple interest

Simple interest is paid as a fixed percentage of the original amount of money you lend or invest (AKA the principal ).

Here’s a simple example.

If you lent £100 to your friend at 10% simple daily interest, they’d owe you £10/day, for as long as the loan remained unpaid. If they paid you back after 7 days, the final bill would £170.

Looking at investments, this is also the kind of interest paid on fixed income or bonds, where the interest payment (coupon rate) is usually a fixed percentage of the face value.

Compound Interest

This is much more… interesting.

With compound interest, interest is paid on the original sum plus the past interest. It’s basically interest on interest. With debts, this can make a big difference.

Take that generous £100 loan. If you were wily (and didn’t care about losing friends), you could charge 10% interest, but compounding daily.

“Hahahah… I want my money, Karen”

Each day of the loan, the interest would be calculated as a percentage of the original money and all the past interest so far.

After day one, they’d owe £110, the same as with simple interest. But after day two, they’d be charged 10% of £110, to bring the total to £121.

After 7 days, your friend’s total bill would be £194. Plus dry-cleaning costs after they throw their coffee at you.

Compound returns

Compounding really comes into its own with investing returns. That’s because returns on your initial money you invest can then grow themselves. With the help of time, compounding growth can turn a modest initial portfolio into a sizeable hoard.

Compounding means you have a very good chance of outperforming Warren Buffett over the next 40 years. Why?

Well without being harsh, it’s because you’ll almost certainly outlive him. Especially if he keeps eating ice cream for breakfast.

To take a dramatic example, let’s say you manage a solid but not spectacular 5% annual return on a £10,000. Assuming you keep your gains invested here’s what you’d make over the years.

This makes a lot of sense when you think about it. After all, when you invest, you’re taking an ownership stake in real companies. And if a company grows 5 years in a row, each year it’s growing from a better position than the last.

You can check out our compound return calculator to have a look at potential returns on your portfolio. You can duplicate the sheet to do your own calculations. Just plug in the annual return you’re targeting, the initial money you’ll invest and the money you’ll add to your portfolio per year.

Bear in mind that, much like an inept darts player, you may not hit your target. You can also use our calculator to look at the same performance with a broker who charges fees. :thinking:

Compound return of the same portfolio with a free Freetrade account vs a broker charging 0.45%/year

Compound interest combined with time can be very powerful. According to one study, ten years of actively adding money to your portfolio followed by 30 years of passive compounding outstrips 30 years of actively adding money and growing at the same rate.

Having 40 years of compounded growth would be better than 30, even if you kept adding more money each year in the second scenario.

So what does this mean for me?

The longer you’re investing, the more years you have to grow. If you do want to start building a portfolio, the earlier you start, the more time you have to compound.

If you procrastinate with your investments, you don’t just miss out on potential returns, you also miss out on the returns of those returns. And then the returns of those returns, until you’re stuck in a spiral of opportunity cost and general annoyance.

Time is pretty much the only finite resource you have as an investor — no-one’s getting any younger. Apart from Hugh Jackman.


80 years young

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Nice!

To do this “Just plug in the annual return you’re targeting, the initial money you’ll invest and the money you’ll add to your portfolio per year” you’ll either need to make your own copy of the spreadsheet (or Toby will need to give everyone write permission :slight_smile: )

Inflation will drag on those returns in the same way that broker X’s fees will. The 149,744 will feel like less in 40 years, unless we’re putting inflation-adjusted interest rates in :balloon:

Don’t expect your actual portfolio to behave like that, a smooth line curving upwards. :chart_with_upwards_trend::chart_with_downwards_trend::chart_with_upwards_trend:

Most investors experience less of a snowball effect than these charts suggest because when their investment horizon is 40y they earn less and have less cash to put to work, so they may need to put more cash to work in their later higher-earning years. :frowning:

… Some of those might be small caveats worth adding to the post, but none of them diminish your main point: if you want the invested money to do some of the work for you, the best time to start investing is always as early as possible. :+1:

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Great points @rod. I’d say duplicate the sheet - or one person’s tweaking could confuse everyone.

We actually considered adding an inflation adjusted sheet in there, but chose not to because:

a) It adds a layer of complexity
b) Inflation rate is never a sure thing, especially in the UK right now :sweat_smile:, so it would have to be another variable

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Maybe a simple proxy for inflation-adjusted interest rate/stock market return would be setting the default % in the spreadsheet to 1.04 rather than 1.07 :slight_smile:

The spreadsheet does show power of compounding and long-term investing.

I think it need more clarification on the 0.45% fees at least some example (I’m guessing this particular one is for ETF). And also how can one achieve 0% fees with Freetrade? Some example would be great.

0% fees is in reference to the fact that we don’t charge any custody fees. Many brokers charge an annual % fee on the assets you hold with them - we don’t. It’s not a fee going to the fund - it goes to the broker.

To invest without paying a penny in fees with Freetrade, you could use a Basic account and only Basic orders.

With our ISA, in April when we start charging, you’d pay a flat £3/month fee. Your fee would never grow as your portfolio grows.

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The rule of 72 explained and a nice video on compounding. :chart_with_upwards_trend:

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Good read:

"Compound Interest applies to EVERYTHING

Everything – money, relationships, health – everything.

The gains in one aspect of your life will compound into other areas of your life.

If you work on your health – it will improve your body – which will improve your personality – which will improve your relationships – improved relationships improve your social and professional network – which in turn improve your cash flows – the extra money frees up time – which can be used to network / build another business / or be spent in the gym – and the cycle goes on.

If you’re smart and understood the above paragraph – you’ll see that the cycle can start at any point you pick."

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How the ‘magic’ of compounding investment growth has its dark side

What a misleading title. It’s just a Etf provider saying that passive is better than active investment. The whole article has nothing to do with compounding really.

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Compounding Fees.
Don’t want to compound your fees - Use Freetrade :freetrade:

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Bumping this educational post in case anyone is looking for a nice Sunday evening read. :newspaper:

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‘Read it’ - done :slight_smile:

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I was just about to write a similar blog post about compounding. I have tried the sheet, but things are looking a bit funny. Hopefully, someone can explain it…

I am using the following in my sheet: =current ETF value * (1+ ( potential return % / 1)) I got the formula from here I then drag the formula down the sheet.

  • I am using £20k as an example.

I haven’t included the lump sums I would be putting in throughout the year. Just the returns…I am following this yearly return example:

Now I know there wont be a return of 19% each year. But it’s only a guide…

This is what I have got as a result in my sheet:

My questions are…

  1. Why does the sheet in this post give me massive results? Am I calculating something incorrectly?
  2. Should I add lump sums into the formula?

I plan to keep the 4 ETFs as long as possible and reinvesting the dividends and profit from this across the 4. This will work better once fractionals come into play.

Have i calculated it correctly or am i missing something?

Seems correct. But 19% is way too high. Also dividing by 1 doesn’t do anything mathematically.

The results are correct. The reason they look so massive is because a 19% annualised return is unrealistically high. You are also assuming no years in the next 20 return a negative.

Usually 7-8% is a more realistic long term annualised return including dividends so I would recommend using that if you are trying to display a rough indicator as to what £20K will be worth in 20 years.

Nothing wrong with your calculations, that is simply how incredible compounding is.

I arrived at the same number:
20k lump sum invested for 20 years at 19.62% annual return
= 20k*(1.1962^20) = ~£720k

The trouble is, 19.62% is a very optimistic long term return. Throughout history, the global stock market has returned 5-10% (usually around 5% after inflation, i.e. in real terms) in the long term (over 20 years is considered a reasonable horizon).

Realistically though, most people drip feed (which has the added benefit of pound cost averaging) rather than investing a lump sum because no one gets paid a lifetime’s salary on the first day of their job . This is where it gets a bit more interesting to calculate, e.g. accounting for sequence of returns risk (where the volatility of your portfolio, or rather the ‘order’ of your returns can affect what you end up with).

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Thanks for the answers @SebReitz, @Kezberg and @sparklesandsweat. The 19% was just used as it was chucked out from justETF but yeah 19% seems too high…

But glad the calculations have been confirmed.

Fundsmith has an annualised return of 18% currently, although wherever they can keep this up is anyone’s guess.