### Albert Einstein described compound interest as the ‘eighth wonder of the world’. “He who understands it … earns it. He who doesn’t … pays it”. In this post, I’ll recap the power of compounding and the Rule of 72 when it comes to personal investing.

**Compound interest** *(or compounding interest)* is the interest calculated on an initial investment amount *(or principal)* and which also includes all of the accumulated interest of previous periods. Compound interest can be thought of therefore as **‘interest on interest’** or **‘returns-on-returns’** and will make a sum grow at a faster rate than **simple interest**, which is calculated only on the original amount.

But, moving on from technical definitions, let’s look at compounding by way of some simple examples.

## Sally & James

Let’s use best friends **Sally** and **James** as our compounding guinea pigs. They are both **19 years of age** and, having become bonafide believers in all things **financial independence**, decide that they want to start thinking about saving for retirement – how very wise ðŸ˜‰

Taking a standard retirement age as their guide, they decide the big day will come on their **65th birthdays** which are just a few days apart.

## Same Goal, Different Approach

While they have a **shared end goal**, they each decide to approach how they get there differently.

Sally plans to **invest a total of Â£16,000**, while James plans to invest a much larger amount of **Â£78,000**. Using different investment strategies and amounts of money, who will have more money come retirement age?

Letâ€™s also assume that both Sally and James will **achieve the same rate of return** *(i.e. the gain on an investment expressed as a percentage of the original amount invested).*

In this example, the rate achieved by both will be **10% per year**. So if they each invested **Â£1,000 today**, they would **earn Â£100** on that money after one year.

So, instinctively who do you think would earn the most money by retirement age?

While James might appear the obvious choice, since he has the most money to invest, via the **power of compounding** we can show how Sally can end up with more than James.

## Crunching the Numbers

Using a **trusty spreadsheet** to map out our example, it will be easy to see who has saved more money. Below we have **columns** for Sally and James. Again, weâ€™ll stick with the **10% per year rate of return**.

Here is the initial portion of the spreadsheet and straight away we can see an initial **difference** in the respective investment decisions adopted by Sally and James.

Sally decided to **drip-feed her investment straight away** at **19 years** of age, while James decided to **delay his investing** until he was **27 years old**.

So, Sally invested **Â£2,000** **at the age of 19** and earned her 10% return on that money by the end of year 1 – **Â£200 earned for a total value of Â£2,200**. At age 20, she invested another Â£2,000 and earned her 10% return on both the new Â£2,000 contribution plus the Â£2,200 from the previous year for a total of **Â£4,620 at the end of the second year**, and so on, and so on.

**Sally used up her allocated Â£16,000 at the age of 26 and had no more money available to invest**.

James, on the other hand, began his investments at **the age of 27**. After the first year, Jamesâ€™s total value was **Â£2,200**; after the next year it was **Â£4,620**, and so on – just like Sallyâ€™s returns at those same points.

## The Midway Point

Letâ€™s fast forward through time towards their **40’s**. Sally and James meet up and decide to **compare their respective investment progress**. Let’s see how they are getting on:

At 40, Sally had long since invested all of her **Â£16,000**. By the same age, James had invested **Â£28,000 of his planned Â£78,000** and was still diligently adding his **Â£2,000 per year**. Yet, it was **Sally who had more than Â£30,000 more than James **at age 40.** **

Even a decade later, at **age 50**, and with James having **added a further Â£20,000 to his investment**, it was **Sally that had more than Â£50,000 more than James. **

Letâ€™s roll on again to the end of their journey – that grand old age of 65 and **retirement day!**

## Retirement Day

Despite not investing anything further since the age of 26 *(and only investing Â£16,000 in total)*, Sally ended up with **more money than James** at age 65 with a grand total of **Â£1,035,160**.

James had been putting in his Â£2,000 each year since age 27, yet he only ended up with **Â£883,185** at age 65 *(despite having invested nearly five times more into his investment than Sally).*

## Time is Your Friend

So, Sally’s decision to **start early** proved to be the overwhelming factor in achieving her superior returns, overcoming the fact that James had significantly more to invest. It was the **returns on her returns** *(or the **compounded returns**)* that enabled **Sally to amas over Â£1m.**

That is the **power of compounding in a nutshell** and why **time is your friend** when investing and why starting early is so beneficial.

## What if…

For comparison, look at what happens if Sally had kept on investing her Â£2,000 each year all the way through to 65. Sally would have invested **Â£94,000 in total** compared with **Jamesâ€™s Â£78,000.**

How would a relatively **small difference of only Â£16,000** spread over 46 years impact the numbers?

Well, the power of compounding is such that this seemingly small, nominal difference of Â£16,000 **translates over time to more than a Â£1m advantage** for Sally by the age of 65!

So hopefully this is a **powerful way** of showing how compounding really is the **8th wonder of the world** and puts **‘time’** to work on an investors behalf.

Here is another example of the **power of compounding**. The graph below shows just the **annual returns from a Â£1,000 investment earning 10%, compounded annually**.

Notice how, **from year 9 onwards**, most of the total yearly return is coming from the **returns on returns** *(i.e the compounded returns)* versus the return on the initial investment.

Itâ€™s clear that, in the early years, the compounded return *(blue bars)* is relatively low, but by year 9, it accounts for more than half of each yearâ€™s return, and the proportion that it contributes **accelerates significantly thereafter**.

So is 9 years some kind of **magic number?** No quite no, but another way of seeing the power of compounding is through whatâ€™s commonly known as the **Rule of 72**.

## The Rule of 72

This rule allows investors a way to * quickly estimate* how many years it will take for a compounded investment to

**double in value**. The rule is as follows:

72 divided by the rate of return = years to double

So, using this rule, if an investor earned a **10% rate of return on a Â£2,000 investment**, his investment would double to **Â£4,000** in roughly **7.2 years**. Knowing this formula allows you to swap any combination of rate of return and/or initial investment to determine the speed at which it should double in value.

Here again we see the power of compounding, By increasing the rate of return from just **1% to 2%**, the investor decreases the amount of time for the investment to double from **72 years to 36** *(i.e. half the time needed)*; by increasing the return from 2**% to 6%,** the doubling time is reduced by **24 years **and so on…

So what seems like a **modest increase in return** produces quite a **dramatic decrease in the doubling time** – all thanks to **compounding**.

As a general formula, the Rule of 72 works best for investments that **compound annually**, meaning that the return is paid to the investor once a year, typically at the very end.

Of course, if compounding occurs **more frequently** than annually, this only serves to **speed up the compounding** process further. Investments might compound quarterly, monthly or daily.

## Monthly vs Yearly Compounding

What if returns were paid monthly instead of yearly, as shown below in the chart with a Â£1,000 investment, earning 10% per year.

It shows that if the return is paid more frequently, then compounding can start working for you sooner, resulting in a **higher overall return**. It also **reduces the time**

“E.g. an investment that is earning8% compounded annuallywould be expected to double in valueroughly 9 years.”

Although **not a dramatic difference**, that same investment compounding monthly, would reach its doubled value about **3 months sooner**. So the **reduction in time is not as dramatic as what you see when the rate of return is increased**.

I hope you enjoyed this post. I think it serves to remind us that some of the most powerful concepts are the often the simplest to grasp.

Until the next time

Dan

## This Post Has 3 Comments

## Caveman

6 Jan 2019Great reminder Dan. While 10% is punchy as you point out the basic maths makes sense at whatever rate of return you hit.

This is something that I’ve been thinking about a lot in the context of my children and whether I should start a pension for them. They aren’t that young but if I can put in a hundred pounds a month into an index tracker for the next few years then the magic of tax free compounding should mean that they have a solid start to their pension savings. They may thank me for it in half a century or so!

## Pursue FIRE

6 Jan 2019Thanks for commenting Caveman – 10% annualised seems like a dream given events of the past few months, but 8-10% has been possible over the long-term. Really the point of this post was not about the return of the investment itself (seeing as both Sally & James receive the exact same return), but to illustrate the time component and how starting young really is incredible. I have another post coming which deals with kids specifically – if you put Â£5k aside for your newborn child into an investment yielding 10% per annum, with no further investment, it would grow to Â£1m by the age of 65. I had put a similar sum aside for each of my three when born, but into JISAs rather than SIPPs (which may have been the better decision in hindsight) as once they hit 18 it’s their money to do as they please. Hopefully, by then, I’ll have them well-trained on delayed gratification and the thought of seeing a large retirement pot will outweigh wanting to spend it all on a rusty old car! ðŸ™‚

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