A Brief History of Time: Compound Interest

People are living longer and longer. Back in the Victorian times, you will be lucky to make it past your 40s. 3 of my grandparents are still alive at 70s, 80s so given the average agesof my grands and ever growing medical and  technological advancements, I estimate myself living to my 90s barring any natural disasters or personal misfortune.

Now I hope I am not going to need to work for a living when my joints grow old and creeky and become deaf as a bat so I have got to plan for my financial escape!

What? Planning for the retirement fund 40-50 years in advance? Isn’t that too early?

I don’t think so and let me introduce you to the 8th Wonder of the World, Compound Interest. Taking 50 years as the average working lifespan of the average person, let’s see what compound interest can do for us.

CI graph
Compounding 100/200/300/400 monthly savings for 50 years with 5% Annual interest

Consider the following scenario,

Starting from Zero Savings,

  • Saver A saves £1200 at the end of Year 1, and at the same rate for the next 49 years
  • Saver B saves £2400 at the end of Year 1, and at the same rate for the next 49 years
  • Saver C saves £3600 at the end of Year 1, and at the same rate for the next 49 years
  • Saver D saves £4800 at the end of Year 1, and at the same rate for the next 49 years

Factoring in an annual interest rate of 5% and assuming all interest remains within the savings pot and not withdrawn, at the end of Year 50,

  • Saver A has £238,112 (From an input of £1200×50=£60,000)
  • Saver B has £476,224 (From an input of £2400×50=£120,000)
  • Saver C has £714,336 (From an input of £3600×50=£180,000)
  • Saver D has £952,448 (From an input of £4800×50=£240,000)

You can see with annual compound interest of 5%, over the course of 50 years, the sum just about quadruples (~3.96x the orginal sum saved). You can just about see that the compounding graph is an exponential equation and if time is unlimited, soon the line would be a vertical line soaring for space! 

Putting it into context, how difficult is it for us to save 100 or 400 per month over the course of our working lifespan? If you have a decent stable job, then it should only be a motivational issue to keep that consistency up for such a long period of time. For many, trying to make ends meet is a miracle by itself, so even 100/month might be difficult. But the point is this, saving any amount consistently over a period of time with compounding interests, you can make the graph exponential and for money to work for you!

5% interest? How realistic is that? The Bank of England base rate and US Federal Reserve rate is still at an all time low of 0.50%. Market savings account interest rate are roughly on average 1-2% with some accounts offering ‘special rates’ with balance limits up to 5-6%. It appears doom and gloom for savers globally. Quantitative Easing (QE) over post 2008 crash have screwed us over. Perhaps it is time to looks at other asset classes to diversify savings. Cash has historically offered the poorest return of all the asset class. Whatever the rate is, the compound effect still hold true (unless its negative rates) and it makes sense to make use of this knowledge.

Next consider this next graph where annual compound interest is 5%

  • Saver A saves 100/month for the whole of 50 years
  • Saver B saves 200/month for the 1st 10 years then 100/month for the next 40 years
  • Saver C saves 300/month for the 1st 10 years then 100/month for the next 40 years
CI 10 years boost
Compounding Savings with savings boosted in the 1st 10 Years

At the end of Year 50,

  • Saver A has 238,112 (3.96x of actual cash saved)
  • Saver B has 339,310 (4.71x of actual cash saved)
  • Saver C has 440,509.9 (5.24x of actual cash saved)

By increasing the ‘pain’ of saving more in the early years, and then easing off, the compounding on the increased savings from the early years really work its magic over the next 40 years to speed up the exponentiality of the curve! In fact, if you can squeeze in as much savings as you can into the early years of your working life, the latter part of saving life will be very much easier.The earlier you plant your seed to grow your FIREplant, the more fruits you have to enjoy later in life.

My Notes

  1. The Snowball Effect
    1. Notice that the first 10-20 years of savings might appear to be a linear graph, but after year 20, the graph becomes more noticeably exponential. Let me give you a horticultural analogy: Your plant a seed to grow a FIREplant. When the FIREplant matures and produces fruits and in turn seeds. You harvest the fruits and replant the seeds back into the soil and grow more FIREplants. The new FIREplants will produce even more fruits and even more seeds. You repeat the same, year after year and in no time, you will have fields and fields of FIREplants, more than you can ever need and it all started with that one seed! Time is your friend in this case.
  2. All You need is Time
    1. Look at the Forbes Rich list 7 out of 10 in the top 10 list are over the age of 70. I wonder how much of their wealth is due to compounding their gains over and over again over their decades. Interesting to note, the other 3 who are under 70 years old are masters of Microsoft, Facebook and Amazon. So the key to growing rich, live for a long long time.

Takeaway Messages

  1. Saving/Investing – Start Early to leverage the compound effect
    • The best time to plant a tree is 20 years ago. The second best time is now.

  2. Keep a Steady Contribution
  3. Reinvesting Interest Earned
  4. Stay Healthy and Live a Long Long life.

So Start Growing Your FIREplant Today! 😀

N.B. Try out Monevator’s excellent Compound Interest Calculator to see how fast the snowball grows!

What is your Savings Rate?

The causal saver might be saving for the next purchase; a car, a sunny holiday destination, a house, the latest electronic device. But item after item where does that end? Let me provide you with a new goal, saving for your Independence!

The single most powerful measure of how you are doing financially and best indicator of how far off you are to financial independence: Your Savings Rate.

Savings Rate: (Annual Savings*/Annual Income) x 100%

*Where Annual Savings= [Annual Income-Annual Spending]

Simply, if say you are spending more than what you are earning, i.e. more than 100% of your income, you will never be able to retire and will technically be in debt.

On the other hand if you are spending only a tiny proportion of what you are earning, for example, 40% as an example, you are still financial dependent on your income but have shown that you can survive on much less than what you earn and you are a net saver (SR = 60%).

Now the magic starts here. If…If somehow your annual spending is zero, you are technically no longer dependent on your income to live and you can retire right away, continue living your free life. If you are one of the lucky few like me, this happened when you were a kid.

The reality is all of us are somewhere on the spectrum of savings rate. We earn and spend a proportion of our income (hopefully less than our income) and save the rest. Now the interesting thing is, the amount that we stash away each year can earn some money on itself (savings interests,CD interest, Bond yields, rental yields, stock dividends, investment yields, etc). As we save more each year, this income from savings can snowball year on year into something significant and if it approaches the level of our annual spending, we can be less reliant on working to earn an income to live. If it breaches the threshold of our annual spending, we are officially financially independent and can rely on this passive income to live.

years_to_retirement
Years to Retirement vs Savings Rate*

*Assumptions

  1. 4% Withdrawal Rule – you will be withdrawing within 4% of your entire stash to meet you annual spending during the decumulation phase (retirement)
  2. Your savings are invested to generate a growth of 5% annual return.
  3. Your stash is meant to last forever.

Someone really clever (?MMM)  came up with the graph above which shows if you are able to achieve an annual Savings Rate of 64% with the above assumptions, you will be able to retire in 10.9 years time. The following table shows the number of years it take to achieve FI with the corresponding savings rate.

Savings Rate Years To FI
10% 51
20% 37
30% 28
40% 22
50% 17
60% 12.5
70% 8.5
80% 5.5
85% 4

My Notes:

  • What I like about the savings rate is it is universal to everyone from the ‘rich’ to the ‘poor’. It applies equally to the high flier who brings in an annual income of £1,000,000 vs the poor city worker who only earns £20,000. Even if you earn an infinite amount of zeros, if your SR is 10%, the reality is you still have to work up to 51 years to become independent. Conversely, if you can achieve a high Savings Rate (70%) on any salary, you will be achieve FI in 8.5 years!
  • Another note about the savings rate is that it includes the element of relative frugality to the equation. It implies that if you can survive on a lot less that what you earn, you will get to financial independence a lot quicker. Most people put a lot of focus on increasing your pay/income, but it works a lot faster if we can reduce our spendings relative to our income. 
  • There has been a lot talk about about savings rate on the personal finance blogs around. The best post about this are Mr Money Moustache’s  The Shocking Maths behind Early Retirement and Monevator’s How to work out your financial independence plan. Both posts are a good read and backs up the assumptions with historical data, analysis and many more references.
  • It is still worth taking a step back and realise this is just a model with arbitrary numbers. It might not be the perfect model (is anything perfect?) but it gives us the encouragement that mathematically the concept is sound and achievable. We just have to take action and use this as basis of our grounding principles to FI.

 

So how far are you till Financial Independence?

 

The world is much more than I.

Greece
Refugees in Greece. Mum feeding kid along railway tracks Photo: Tobias

Sometimes it is so easy to get caught up in work and life rolling on. Seconds become minutes, minutes becomes hours, hours become days, days become weeks, weeks become months and then years and decades and at some point people reach a point when they pause and think ‘what’s the point of all this?’ ‘Where is the end?’ (Midlife crisis?) I think we all have our mini crisis on a daily and weekly basis hence needing to look forward to happy hump day and weekends!

Well we are lucky that time flows in one direction and all things must come to an end (sounds morbid I know), but that means all things good or horrible will not last forever. So we should just enjoy the view, appreciate the tears of joy and sorrows along the way and consider that everyone else is on the journey as well. It is one reason I enjoy stories, real or fiction reminding me there are others out there feeling the same worldly frustrations or wonders. Reflecting on other people’s stories also reminds you that the world is much bigger than your five senses or your internal narrative.

Hence the photo narrative can hopefully be a therapeutic break for the mind. The world is much more than I.