The power of compound interest.

It’s a concept we hear about regularly, and perhaps you’ve known of it for years.

Even Einstein allegedly commented on it:

Compound interest is the eighth wonder of the world. He who understands it, earns it. He who doesn’t, pays it.

Albert Einstein

And as with everything Einstein, there’s a lot of truth in his statement.

But, according to ValuePenguin (valuepenguin.com), 69% of Americans don’t understand compounding. And you can bet your boots that here in the UK, we’re likely in a similar situation – I certainly didn’t learn about it in school.

In fact, I didn’t fully get it before beginning to invest, and I made it my mission to grasp the concept of compounding. And now I do understand it, I’m making it my next mission that my children will too.

So, if you’re still confused about compound interest, you know what? You’re not alone.

Yes, it may have been advantageous to have learned about it sooner. But, then again, if you’re a small business owner…

…I don’t think you’ve been missing out as much as you may think. If at all.

You see, as with everything in life, there are trade-offs. And with every good bit of magic that happens in one place, perhaps a little dark magic is done elsewhere…

You get the gist!

Now, read on for* *compound interest explained, the good and the bad.

## What is compound interest? It may not be what you think…

Before I talk about compounding interest – or the phenomenon known as compounding – it’s useful to be familiar with the idea of simple interest because until you receive this first simple interest payment, you can’t start to compound!

I’ve read so many articles about compounding where the writer has – inadvertently – given the wrong idea about compound interest by not making the distinction from the simple interest each time an interest payment is made.

### So, what’s the difference between compound interest and simple interest?

Many people I know are happy with the principle of earning interest on their money in the bank.

In other words, if you leave some money in the bank for a period of time, say one year, the bank will pay you a small percentage of that money for keeping it there. [And at the time of writing, it is **very** small…]

This payment is known as simple interest and the initial amount put into the bank is called the principal.

Once you’ve received this interest payment, you can do one of two things with it:

- Take it out, or
- Leave it in.

If you decide to take it out and leave your principal amount in the bank for another year, the bank will again pay you simple interest on the principal amount of money. (It’s this that’s often not clear.)

However, if you decide to leave the simple interest payment in your account, when the bank makes its next interest payment to you in one year’s time, it pays you interest on the total amount in your account – your initial principal amount **plus** the interest you received from that first year.

This latter payment is called compound interest, or interest on interest!

Over time, the compound interest accumulates, and if you’ve enough money saved, it can cause the money in your account to snowball!

I’ll use an example to illustrate what’s going on.

If you invest £100 into a high-interest savings account paying 3% annual interest, at the end of Year 1, you will have the £100 plus the interest earned, 0.03 x £100 = £3. This gives you a total amount of £103 in your bank account at the end of this first year.

If you decide to leave both the initial principal amount **and** the simple interest gained in the account for another year, in other words, the full £103, the amount of interest at the end of the second year is £103 x 0.03 = £3.09. This leaves you with a total amount of £106.09 in your account after the second year.

This table breaks it down more clearly:

Principal amount (original investment) | £100.00 |

Simple Interest for Year 1 (£100 x 0.03) | £3.00 |

Simple interest for Year 2 (£100 x 0.03) | £3.00 |

Interest on interest for Year 2 (0.03 x £3.00) | £0.09 |

Total | £106.09 |

One of the things to note about simple interest is that it’s earned each period. I don’t think that this is always clear in articles about compound interest.

It is the interest on the interest – the 9p in this case – that is the compound interest.

Simple interest is hugely important. However, for a given interest rate, it is always fixed from period to period, for example, from year to year or from month to month.

Compound interest is far more powerful because although the initial amount may be small, it grows in size each period. In addition, the power of compound interest works best when the interest rate is large.

For example, after 20 years, your initial £100 deposit would be worth £180 if compounded annually at 3%. However, it’d be worth £265 if compounded annually at 5% over the same timeframe.

This is the power of compounding in action, and it works by growing your wealth exponentially. The profit earned is added back to the principal, and the entire sum is reinvested, accelerating the profit-earning process. In effect, your money is working for you.

The magic of compound interest is time. This is why it’s best to start saving or investing early.

### Start saving now! Think of the children…!

I’m obviously being overly dramatic here, but so many articles on compound interest tell you to start saving early. And for a good reason because it’s good advice for savers.

To* *find power in compound interest*,* we *need* to start saving early.

If you haven’t already started a savings or investment account for your children, it’s probably a good idea to consider one because **when** we start saving can outweigh **how much** we save.

Starting saving early will maximise what we can do for our children with their money. If you can afford to put away a chunk of money, eventually, it could add up to a decent amount, even if you don’t add any more to it.

The following example shows how compound interest works, with an initial lump sum of £10,000 put away for up to 50 years at an average 7% interest rate.

So, £10,000 will be worth £38,696 in 20 years when investing at an average rate of return of 7%. This is also how the same £10k investment becomes £294,570 at a 7% return in 50 years!* *

I know at first these figures seem unrealistic. You may even be thinking, “How on earth can I save that much?”

It’s worth remembering that according to IG, the FTSE 100 – an index of the 100 biggest companies in the UK – has returned an average of 7.75% since its inception in early 1984.

These types of gains really do make compound interest a reality for you.

Indeed, I think that putting a chunk of money in a tracker fund could be *o*ne of the best ways to save for retirement and is one of the great ways of building wealth for the long term.

You’ll notice from looking at the graph that the largest increases occur during the later years of the investment. This is exponential growth. Patience and a long-term perspective are so important!

Always remember that banks don’t offer compound interest on deposits. You receive compound interest by reinvesting it – leaving it in your account.

## How to Calculate the Power of Compounding in Your Investments

If you already have investments or savings, you may be wondering how to calculate compound interest in your own portfolio.

I use a Texas BAII Plus financial calculator to do this because, although it’s not cheap, calculating compound interest is only one of many things I use it for. However, the other benefits of using one are being really easy to use and very quick. That said, there are various compounding calculators online that do the job, and even better is that they’re often free.

A compounding calculator computes the value of an investment after a certain number of years and at a specific interest rate. A good one will also allow you to enter additional deposits and is able to adjust the frequency of your compounding, which I’ll explain shortly.

To use a basic compounding calculator, you need to know:

- The number of years you wish to invest (N)
- Your interest rate, or an approximate rate at which you’ll be investing (I/Y), and
- Your initial investment amount, the principal (P)

Once these figures are known to you, enter them into the correct fields and the calculator will do the rest.

But, like any other application, we need to understand how the calculator does its sums to make sure we’re on the right track – in other words, we need to understand the general compound interest formula. And if you can get your head around this, you won’t even need a compounding calculator!

Here:

A = future value of your investment (or loan)

P = your principal amount

r = interest rate (in decimal format)

N = number of compounding periods

Always remember with this equation that both N and r must use the same time units. For example, if N is in months, then your interest rate must also be the one-month rate and not an annual one.

So, with our previous £100 investment example,

A = £100(1+0.03)^2 = £106.09

In the 5% over 2 years example,

A(20) = £100(1+0.05)^20 = £265.32

So long as you remember to use the same time frame, you’ll be all over compounding!

### How the frequency of compounding changes things

Now you’ve got the basics, it’s time to shake things up a little!

Sometimes, you may see offers of products using interest rates that compound more than once a year. For example, banks may offer a monthly interest rate that will compound 12 times per year. In other words, you get paid interest every month.

But, a bank may not use the term ‘monthly interest rate’ when advertising a product. They often use the terms **stated annual interest rate**, or **quoted interest rate** instead.

(Be aware when they use the terms Annual Percentage Rate, APR, that you know exactly what this entails because its exact meaning varies. Don’t be afraid to ask exactly how interest is calculated on a product – it’s **not** a stupid question. It shows understanding. Likewise for the terms equivalent annual rate or annual percentage rate. )

For example, a specific account may pay interest at 7% compounded monthly. The stated annual interest rate is the monthly interest rate divided by 12. So, in this example, it is 0.07/12 = 0.0058 = 0.58%. [The rate doesn’t sound so good now, does it?!]

When this happens, and you want to calculate the future value of your investment, make sure you’ve used the interest rate for your chosen period, and that your number of periods (N) is the correct number of periods for that rate.

You do this as follows:

- When you use more than one compounding period per year, you need to make sure you divide the stated annual interest rate by the number of compounding periods in that year to give you your periodic rate.
- You must also make sure you multiply the number of years by the number of compounding periods in one year to give you the total number of compounding periods.

For example, a bank offers you an account where for 2 years, you receive a stated annual interest rate of 4%, compounded monthly. To find the value of your account after that two-year period and with an initial deposit (principal) of £100:

The periodic rate of interest = 4% divided by 12 (since interest is 4% per year, and is compounded monthly – there are 12 months in a year), 0.04/12 = 0.0033

The number of compounding periods = 2 years x 12 periods per year = 24 periods total.

P = £100

Now put these numbers into the general compound interest formula:

**A(n) = P(1+r) ^N**

A = 100(1+0.0033)^24

A = £108.22

For comparison, using annual instead of monthly compounding gives you a total of £108.16.

At these smaller savings amounts, we’re talking a difference of pence. However, when you’re using compounding for bigger investments, or loans, the difference is much more noticeable.

### Compounding ad infinitum! (a.k.a. continuous compounding)

All the previous examples of compounding have used discrete compounding, where interest is paid after a very specific chunk of time, or period.

However, sometimes the interest is compounded on a continuous basis – all the time – rather than over specific time periods. This is known as continuous compounding, and it’s something we need to be aware of.

(I’m not going to go into how it’s calculated as it involves logarithms, and most people go cross-eyed and look at me like I’ve got two heads. If you’re interested, google it!)

However, this table shows exactly what I mean:

Effects of Compounding on Future Value | |||

Frequency | Periodic Rate | Number of periods | Future Value of £1 at end of year 1 |

Annual | 6%/1 = 6% | 1 x 1 = 1 | £1.00 (1.06) = £1.0600 |

Semi-annual | 6%/2 = 3% | 2 x 1 = 2 | £1.00 (1.03)² = £1.0609 |

Quarterly | 6%/4 = 1.5% | 4 x 1 = 4 | £1.00 (1.015)⁴ = £1.061363 |

Monthly | 6%/12 = 0.5% | 12 x 1 = 12 | £1.00(1.005)¹² = £1.061677 |

Daily | 6%/365 = 0.0164% | 365 x 1 = 365 | £1.00 (1.000164)³⁶⁵ = £1.061682 |

Continuous | £1.00e˄0.06(1) = £1.061836 | ||

Future Value on £100,000 | |||

Annual | 6% | 1 | £106,000 |

Semi-annual | 3% | 2 | £106,090 |

Quarterly | 1.5% | 4 | £106,136 |

Monthly | 0.5% | 12 | £106,167.78 |

Daily | 0.0164% | 365 | £106,168.26 |

Continuous | £106,183.65 |

So, the difference between compounding annually and compounding continuously over one year is 18p for the £1.00 example but £183.65 for the £100,000.

The more frequently we compound, the larger the end result. This is exactly why saving as much as you can for as long as you can is the best route to riches!

However, it’s why loan providers also like continuous compounding because it’s the best route to riches for them too.

Banks will often use the term **effective annual rate, (EAR) **when marketing loans. This is different from the stated annual interest rate.

You’ll note that an investment of £1 at 6% over the course of a year in the real world will pay the same interest whether it’s compounded annually or semi-annually (£1.06). One reason is that we don’t use fractions of pennies anymore for currency.

However, it also means there’s a technical difference between the stated annual interest rate, and what is being paid. In this case, the EAR for semi-annual compounding is 6.09%, although the *stated* annual rate is 6%.

Like discrete compounding, this isn’t too noticeable with smaller amounts over short periods. But, if you’re borrowing larger amounts and paying them back over a long period of time, as with a mortgage, this form of compounding will add up in your payments.

## The advantages of compound interest for mumpreneurs

If you’ve read my whole guide so far, the benefits of compound interest* *are probably fairly obvious to you.

The big one, of course, is that you maximise the returns in the principal amount of money you’re saving or investing.

But for me personally, I think the benefits of the latter are far greater because I invest greater amounts of money than I put into a savings account. Dividend investing – or buying dividend stocks – is my favourite way of doing this.

Dividends are small chunks of money that a company pays out to its shareholders from its annual profits. Some companies will reinvest this money to grow, but often more mature companies will pay it out in dividends, as an incentive for shareholders to invest in the company. Quite often, paying dividends is a sign of a successful company.

I like to reinvest these dividend payments back into more shares, either in the same company or another one. Over time, this allows my investment portfolio to increase exponentially. Which I like. A lot. (Only always remember, if the company doesn’t make a profit, it can’t issue a dividend.)

The accumulation of dividend payments uses the principle of compound interest and is a long-term return driver.

To put this into perspective, a Bloomberg article I read recently stated that over the 10-year period to the end of 2016, the FTSE 100 (an index of the 100 biggest firms listed on the London Stock Exchange) returned a little under 15% to shareholders when dividends were not included. When dividends were included in the calculation, the return was 67%!

Moreover, according to IG, the FTSE 100 returned a total of 103% to shareholders between 2010 – 2019. Blimey!

This is* *how the power of compounding works in investments. It’s amazing!

## The downsides of compound interest no one tells you about

Despite everything I’ve just written about, under certain circumstances, compounding may not appear everything it’s hyped up to be.

If you fit into one of the following three categories, it’s really important to make sure you understand your own finances completely so you can make an informed decision about taking out a loan, investing, or even saving any money at all! Yes, really.

(An open chat with a financial advisor could be a good idea, but the final decision is always yours.)

### The negatives for borrowers

If you take out a loan, like a mortgage, for example, the main reason for the increase in the interest you pay is compounding. Compound interest works as well for creditors (loan providers) as it does for savers. Perhaps even better.

Once you’ve got the debt, you keep paying the interest until the loan plus the interest has been repaid. So, as long as you have the loan, interest is accruing on the loan** and** your previous interest payments. Ouch!

In this way, continuously compounded loans are far worse for your wallet than annual, or even monthly, compounded ones.

This is why it makes sense to always pay back more than the minimum amount on a credit card balance, or mortgage. If not, the total amount you pay back can be far more than the original debt. Otherwise, it’s easy to get into a vicious cycle of larger debt repayments.

To make things worse, many credit lending institutions will try to encourage you to keep borrowing for longer to pay this additional interest.

So, it makes sense to pay back some of the principal amounts you borrowed each time to keep these payments lower, pay as quickly as possible, and make sure you pay on time – even one additional day will increase the amount you pay.

### The drawbacks for investors

When buying shares, it’s really important to understand why they’ve been assigned the values they have.

At the end of the day, share prices, like any other product, are based on the demand for them. The higher the demand, the higher they go.

But, investment analysts can influence this demand by forecasting certain values of shares. In other words, they’ll recommend you buy a certain share for a particular reason.

When this happens, often investors respond accordingly, and the share becomes more expensive.

However, it’s where we need to be careful.

Investment analysts can use the phenomenon of compounding as a philosopher’s stone to justify any share valuation. They may be very optimistic about the growth of the stock price and provide long-term forecasts about future success.

And often, they’ll be wrong. (I’ve written for a large investing website. This is something I’ve seen over and over again.)

Don’t be persuaded to buy a share if one of the reasons for its attractiveness is based on compounding. (Of course, there may be other solid reasons to buy it but make sure you know what they are.)

#### The beastly nature of compound costs

Unfortunately for us, investments have costs associated with them. These can be anything from trading costs to legal or management fees. However, what they all have in common is money leaving your wallet!

It’s a fairly obvious statement, but the more you pay in investment costs, the lower your return will be. So, we want to keep these costs as low as possible!

Moreover, all those small percentages on fees of any type add up over time and create compound costs. Rubbish.

The sad fact is that all this money leaving your purse adds friction to your magic compounding strategy and slows the process of building your wealth.

The reality of these investing costs is one of the reasons I like passive funds, such as an Exchange Traded Funds (ETF), and also why I love to choose my own investments, rather than paying a fund manager to manage them for me.

#### High risk can mean high return! (But usually not.)

The secret to building wealth via compound interest is getting a good return on your money.

However, the principle of financial markets is the higher the risk, the higher the return. This is for one simple reason – people need rewards for taking big risks, or they wouldn’t take them with their money.

For many investors, this is tempting. But, one of my principles for investing, rather than recklessly trading, is the safety of my principal amount.

In other words, I try not to lose money as much as I try to make money. Perhaps, even more so.

Consequently, I never take those big risks to earn rewards that could really boost my compounded amounts. But, I don’t risk losing it all either because that would kill my compounding stone dead!

#### Changing economic conditions

If you’ve ever looked into the bond market, you’ll note that the returns are better on bonds with longer maturities.

(For those who are unsure, bonds are debt, and usually from governments or large businesses. You lend them some cash, they pay you a coupon – interest – over a period of time. You buy and sell the debt on financial markets, instead of directly from the institution.)

The reason higher interest is paid on bonds with longer maturities is that the distant future is more uncertain. So, the debt is a higher risk because you don’t know what you need to do to mitigate any detrimental circumstances.

It’s easier to understand what’s happening with inflation, interest rates and taxes in a couple of months than it is in 10 years, so you can mitigate your risk. All these factors have an effect on the price of the bond.

Right now, we’re in a period of low-interest rates which is not great for compounding because it means lower returns on your savings and investments.

But, low-interest rates are good for borrowers who want to invest in their businesses.

This leads me to my next point.

### The cons for entrepreneurs that many don’t consider

Entrepreneurs are in a great position when it comes to risk. This is because we have a choice of what we do with our money.

Do you invest your money in **your** business, or in someone else’s by investing in stocks/shares?

The advantage of investing in your business is that you control the risk you take with your money. Investors can’t do this. As investors in other businesses – or other products – via the financial markets, we have no control over the decisions made on our behalf. (NB. You also have flexibility regarding tax payments with money in your business. This is worth looking into.)

It may be that you can earn higher returns from your own business than you can in financial markets, **and** you control the risk.

You can make the most of these returns by growing your business efficiently and profitably. You just have to trust yourself that you can do it!

In many ways, this is far superior to waiting for your compound interest to make you rich.

#### Compounding can be like waiting for Godot – it takes a long, long time

Compound interest can work brilliantly in the long run, says every article that was written about compounding, ever.

But, how long is that?!

From the graph at the beginning of this post, you can see it can takes around 30 years to really get the exponential growth that is the magical power of compounding. That’s a very long time!

Could you be making more money with your business in the meantime?

#### Compounding neglects your cash flow

I’ve written in the past for a large investing website. So, often I found myself writing sentences like “over time the market goes up”, and “average return over time”.

(In fact, see the section on ‘Why it’s important to save now’ for a great example!)

The usual advice is to regularly pop away a little money, and over time the magic of compounding will blow this up into a lot using the average rates of the financial markets.

However, there’s a difference between the average market rate and the actual one.

You may average a certain rate over time, but if one year you’ve experienced a big dip in returns, even if you gain back at the same rate the following year, your average rate is a big fat zero. And you’re still paying investing costs to boot.

For example, if your £10,000 investment loses 10% in one year, you end up with £9,000 at the end. If you then gain 10% in year two, you’re only back up to £9,900. Your average rate over the two years is zero, and this doesn’t include any costs!

However, are you good at what you do – do you get a better return from your own business?

When you invest in your business cash flow, you don’t need to wait 30 years for the magic of compounding to take hold. You can benefit from it now!

And, you can measure it regularly along the way, which can be very satisfying.

## The bottom line…

So, now you’re at the end of my post, do you think Einstein was right?

I do.

Without knowledge of compounding, you can easily be stung with additional payments on borrowed money.

It’s also easy to make a less effective decision on how you use your money.

Alternatively, understanding how to use the magic of compounding **your** way, optimised for your own specific circumstances, is hugely empowering.

I think it can be reassuring to know that if someone else manages their finances differently, then that’s ok. You’re not wrong. You’re likely right for you.

So, go forth! Make it your mission to use your new knowledge to take advantage of compound interest the very best way you can!

**I’d love to hear about how you get on. Let me know below.**

*Related content about economics:*

Wow, Rachael, You have written so well about compound interest. Your article helps you to improve your knowledge of trading. After reading your article I can apply this method in trading.

Hi George. Really glad it helps with the trading. I’m discovering that the more I learn about economics, the more it helps with life generally! It’s absolutely fascinating.