Compound interest is probably the most powerful "force" governing out lives.
It is crucial when borrowing money, especially for longer terms.
It is crucial when saving and investing.
It is crucial in self-development, where a tiny 5% improvement in some area of your life per year can mean that you are twice as good at something in 15 years.
It is important when evaluating any kinds of improvements in personal life or in business.
The trick is that the percentage never sounds like much. The number of years always sounds like a lot. Nonetheless, the years WILL pass whether you want them to or not, and what tiny life choices you make throughout have a huge impact on where you will be in the future.
Being aware of that does not take much. An hour of intense concentration should be enough to get this insight. Of course, this depends on your age and math background. However, I feel confident saying the above as this to the Hacker News audience, as the above requires nothing more than an imagination and the ability to add and multiply by decimals.
Since really grasping compound interest I've noticed it apply across almost all aspects of life, which is what OP is saying. It shouldn't be reduced to the financial aspect which is probably the better-understood aspect of it.
Think about things like your education, your professional skills, your interests and hobbies, your health, your friendship and (professional) social network, hell, even your kids. Whatever little you put into any of these today will compound over time.
If I set some time apart today to better learn a programming language (or a text editor) I will be more productive with it over the next few years. If I develop a healthy exercise and nutrition regimen in my youth, I'll have less trouble maintaining that as I get older and a better starting point. If I try to go out and meet people then I'll have a large network of contacts to draw from if I'm ever looking for something specific in the future. If I've dabbled with a number of different hobbies in my youth then I'll have all these experiences which shape, and ultimately improve the outcomes that I have when tackling a problem today. And lastly kids: If I spend quality time with my kids in their very early formative years (reading, singing, talking) then by the time they enter school they will already have an above-average level of education and that difference will continue to compound for them in their life.
The 'rule of 72' is a quick and easy rule of thumb to determine how long an investment doubles, and improve how you think about compound interest. For example it takes approx. 10 years to double an investment at 7%, or 7 years at 10%.
> The S&P500 with dividends reinvested has averaged a real (post-inflation) return of 7% annually over the last 100 years or so.
TBH I don't think looking at the last hundred years is particularly valuable. Nobody invests over a hundred year timespan. Most importantly, look at a graph of interest rates over the past 40 years. There is a fundamental "new normal" of extremely low rates (or, rather, negative rates for much of the world), making it extremely difficult to earn that 7% without taking on a very large amount of risk.
That's fine if you are prepared to take on significant risk - it took six years for the index to recover after the 2007 financial crash. If anyone was looking to retire on their investment then they'd be screwed. At least with a bank your savings are guaranteed.
It may be true only for the people that have invested ALL their money as a lump sum right before the index crashed (at the worst possible time).
For anybody else, those that say invested in the previous few years into a passive index fund, and continued to invest in the next few years they would have broken even within two years then probably quadrupled their money by today.
Keeping the same amount in a bank would have turned it into 30% less - a decrease similar to what the "crash" would have caused.
The 2007-2008 period was actually the time to invest even more aggressively, if you could stomach it! Historically, those big drops rarely happen. And when they do, they rarely last for long. You have full recovery in a few years. My investments from that time, mostly Total Stock Index funds, like VTSAX, have tripled.
People need to be taught not to be afraid of investing. I know many smart folks, some who are engineers, who were scared of investing until they were in their mid 30's. My dad taught me about investing when I was a teenager. You do this right, you can retire in your 40's or 50's, never have to work again if you don't want to.
You might luck out, maybe hit it rich on startup stock options by joining the next FAANG company. This is unlikely to happen. Investing in the stock market, week after week, year after year, decade after decade... It's almost guaranteed.
> I know many smart folks, some who are engineers, who were scared of investing until they were in their mid 30's.
One of my biggest regrets, coming from a family/socioeconomic group where nobody invested, is not beginning to invest as soon as I had enough disposable income to safely do so (in my mid-20s) instead of in my mid-30s.
Yes! It's too bad none of this is really taught in schools, outside of the occasional "stock market club." It's foundational stuff and people should be educated on it.
That's why fund balance and risk tolerance is a thing. If you're 55+ and looking to retire that 2008 drop will force you to eat cat food. But if you're 50+ most of your money should be in bonds, holding wealth.
If you're 33 and working in IT, you should be holding stocks and hoarding that fantastic growth (and slowly, over time, scraping the gains off into bonds).
You bank savings are only guaranteed by FDIC to $300k. Chances are they are not giving you an interest rate that will keep up with inflation, either. At best it's not gaining value, and is in all likelihood losing value by tiny amounts as inflation eats away at it.
The only problem with that is we are living longer and longer, but wanting to retire earlier... it's really an individual thing, and you have to make sure that whatever you're invested in, you will have the principle + earnings to be able to cover your needs for however long you live.
Keep in mind that costs for elderly care have gone nowhere but sky-high in the past decade or so. It's not crazy to plan on paying 10-25,000/month once you reach your 80s or 90s (or more if inflation rises).
That's why you take on riskier investments early on and transition to "safer" ones as you reach retirement age (or whenever you're planning to access the money).
I always found this slightly wrong (for a non-outlier case). If you're young and you have some earning/saving power, why would you want that to be risky? Keeping it "safe" in an index fund means that it is compounding longer than the assets you'll get later in life!
The confusion is probably coming from your idea of “risk”. When people say stocks are risky they mean their prices have higher variance. But they also have higher long term growth rates. If you’re young, you have more years left until you will need to sell your investments in retirement. That means you should care less about the short term variance and more about the long term growth rate.
Guaranteed to loose value over time. Ever since central banks forced gov fiat currency on us all, we're stuck investing just to save for the future. Back in 1905, most people could save in gold, and very few invested, but now that dollars/euros/yuan saved loose value over time, we're all forced to use equity as a money-substitute for savings.
You are gaurenteeing a loss of purchasing power by putting your money in the bank. You are only risking a potential loss investing in the S&P, and you have a potential significant upside. It's a no brainer.
Risk depends on how long you have until you are going to start pulling on that money. The only people screwed investing wise from 2007 were the people who pulled out. If you can keep a level head, which might preclude some people, investing in stocks is hardly risky. Specifically using index funds, because there is a lot of risk in picking a few stocks.
That’s only if you need almost no risk. The whole US stock market is definitely risky (it could go down fifty percent or more in a year), but it has averaged significantly over 2%, even after inflation, even in the last few years.
This is also noted. Do you consider the downside risk higher than the potential upside over the next 12 months? I am currently viewing downside risk as a higher probability than the potential upside due to a number of macro issues. Plus Warren Buffet just went to a cash pile.
If your time frame is longer than seven years, then it just about always makes sense to leave your money in the market. Even if the market drops 20% in a crash, the market is up more than 20% now since people started majorly talking about fear of a recession a year ago, so it would’ve been better to put money in then than to avoid the market for fear of recession. There might be a recession in a year, but the market’s gains in that time might be bigger than the drop.
Warren Buffett recommends that the best way for the average person to build wealth is to invest in an S&P 500 index fund. Read some John Bogle and you'll get a good grasp on index investing and you'll learn that "time in the market, beats timing the market." Most people get timing completely wrong and end up selling at lows and buying at highs. You're better off dollar cost averaging and investing money consistently over time.
I think a seriously overlooked application of this principle is in nutrition and dieting. Over- or under- eating by a small percentage of your required intake might not have a discernible effect immediately but really adds up over time, both for weight loss and gain.
The fallacy here is that a human body is a machine with well-defined intake and output.
How would one even know what is "exactly" the right amount?
Over a year we consume 1 million calories. If one were just 0.1% off of systematically eating more (or less) than required then according to your model one would end up being 200 pounds fatter or 200 pounds leaner ... do you think that anyone can regulate up to 0.1% accuracy to what they actually need?
eating a little more or less has absolutely not discernible effect the body adapts to it.
0.1% of 1 million calories is 1000 calories, which corresponds to about 0.3 pounds. If someone gains or loses 10 pounds in a year, that means they were around 35000 calories away from equilibrium throughout the year, which is more like 3-5%.
So a 5% calorie deficit or surplus would have a fairly small effect during a single year, but over a decade or a lifetime the effect is huge.
It is exactly how it works, and you're taking "a small percentage" to a ridiculous degree to fallaciously disprove it. Try eating 10% more or less than what you need each day, not 0.1%.
Another question to pile onto this. Maybe you're the right one to ask.
I was always taught that the body uses up its glycogen stores before burning fat. But if that were true even a small calorie deficit would gradually use up our glycogen stores and we'd be walking around without any after that.
Plus before losing any fat you'd have to experience a glycogen crash/wall which most small deficit dieters don't experience.
Generally what fuel your body burns depends on the intensity of work you are doing, so if you're walking you may be burning 80%+ fat, but if you're running a 10k you may be 80% glycogen.
However, if you eat too many carbs at a meal (beyond what you need in the next few hours), your body needs to get that excess out of your bloodstream, so it will do a combination of:
- fill your muscle/liver glycogen stores (limited size)
- burn any excess carbs in preferences to stored fat
- convert any excess carbs to stored fat
Once it's got rid of the excess carbs from your bloodstream, it will return to burning whatever the normal ratio of fat:carbs is for you.
Consequently, if you always eat too much carbs, you'll gradually pile on the fat, unless you're doing large amounts of training which depletes your muscle/liver glycogen, e.g: elite athletes.
No, if that was true people would be always over or under the weight as it's impossible to know exactly how much calories the body consumes.
> Yes, the body adapts to it by storing or eliminating fat (among other things).
No, it compensates by changing your metabolic rate mostly. You eat less, you will feel more lethargic, you eat more and you will fill (and be) more active
In the US, we tend to use food calories, where 1 Calorie == 1 kilocalorie. The capitalization of Calorie is intended to show the difference in units, but in most written language, often isn't used.
To reap the benefits of compound interest (in your favor), you need to stick to a plan. You can't dump your investment portfolio after 5 years. It's these small, daily decisions that add up over time. So while the output is multiplicative, the necessary input is only linear.
If you had to put in compounding effort, the compounding output would seem far less intriguing or worthwhile. If investment returns weren't exponential, or required exponential input to receive exponential output, it'd be far less useful of a concept.
How old are you? My father was thin until he turned 27. He was never huge, but at 27 he was 170lbs (6'2") and at his peak, around age 65, he was a little over 200. He warned me about that. At 27, I was also 170 lbs (6'2") (I am nearly a clone of my dad), and then slowly gained weight. I briefly ballooned to 215 around age 31, but hammered that back down to 185, but since then it has slowly climbed to 200 (at age 60). I am back down to 196. In my early twenties I could eat a large 'special' pizza by myself in about 45 minutes. Metabolism changes with age. I dearly miss being able to eat anything I wanted at any time with no consequences.
When I was in my mid-20s I could also eat anything I wanted, and a big challenge for me was finding pants that were long enough (36” inseam) but also had a narrow enough waist. This was pre-internet, so the options were limited (I discovered early that Big & Tall stores required you to be both).
Fast-forward 20-ish years, and I’m still just as tall but I don’t have any problem finding pants that fit me. Sigh.
Confirm. Went from 165 lbs running 55km races to 235 lbs with a 1,405 lbs powerlifting total in 5 years. I started this month to reverse the process, going to run a 50 miler next time this year.
There is this nice book called "The Slight Edge" which builds on this whole idea in general and how it is applicable at every facet of life. It is really an insightful book and atleast you will slightly change about how you think about stuffs.
I'm reading *Atomic Habits right now and the author talks about how building small improvements on top of each other can eventually deliver great gains. The trick seems to be identifying just what it is to work on.
The way I look at it is compounding just changes the effective interest rate.
Continuous compounding is e^rt. Just subtract straight interest from this and you discover the maximum return of compounding over just collecting interest. Most compounding periods are much less than continuous.
Compound anything is powerful. Interest is... really slow these days though. Seems to be around 3% return after inflation. And with all the countries taking really high national debt, who's to say it will get better?
The whole compound concept applies very well to startups though. 3% a week adds up.
3% is the high-end of the “consumer” (aka “chump”) interest rates.
In fact, since inflation is about 3%, over time your money doesn’t grow. (Though, if you’re earning less than inflation your money is actually decreasing in value, so maintaining is better than that)
Also learn about opportunity cost when spending and saving. It is tied to compound interest in many ways, but also deals with addressing wants vs. needs, and also scoring your wants.
It is true. It is crucial to understand any kind of growth situation which are predominent in life. For instance, one of my friends who is a teacher wanted to explain sustainable development to his highschool students by showing the effect of cutting too much trees if this doesn't match the trees growing rate. He asked me to solve the not so trivial equations with a series and found myself returning to the same maths used for the interest computation.
compound interest is where the bank say's its 3.5% interest but if you do the math you're paying 180% for a house. I don't have any idea how that became acceptable/the norm.
I have many reservations and am very critical of the financial system. But the concept of interest on loans is not a "scam'.
The interest in it's simplest form is just a value appreciation of the time value of money [1]. Would you rather have $100 today, or $100 next month? How about $100 today vs $102 next month? Still rather in the today camp? How about $105 next month? That is the interest. It is the value derivative of having the money 'now' vs having the money 'later'.
Where things can get scammy is in the complex type of credit products on offer (tying in all sorts of opaque references to things presented as neutral which are far from), and how things are communicated to the borrower.
Tip: If you are considering a loan, always ask for a full repayment plan showing you which payments are due each month, and the resulting reduction in the amount due (your payment first covers the interest accrued in that month, and only after that covers principal reduction). If there are variables in the loans formula, ask for simulations that cover the most likely evolution scenario, as well as the extremes. Every financial institution has such a payment plan calculator. Long ago I have written one which afaik is still in use today in a non-trivial financial services company.
Good comment. I sometimes describe borrowing as renting money, where interest is the rent. Its a mathematically interesting construct because, for one thing, the value of the thing you rented goes down with cumulative rent paid. It's kind of a degenerate money cycle if you loan money to someone who uses it to pay you interest on the loan. I suppose only taxes (serving as friction, removing energy) prevent this from being a kind of economic perpetual motion machine! I'd be stunned if this trick wasn't a) very old, and b) have about 1000 modern variations.
I didn't say interest on a loan was a scam I think compound interest on mortgages is. A fixed price interest would make sense like you borrow £100 , you pay back £110. 10% interest. But my understanding on a compound interest mortgage is the bank says something like 2% interest. and they take the £100 and x by 1.02 and just spam ='s on the calculator until the actual interest percentage is like 180%.
You shouldn't have to spend an hour learning how the bank are gnna screw you.
While I appreciate your concern, the problem with what you call 'actual' interest percentage is not what reflects the financial transaction.
As stated above, money has a 'time value'. Getting $100 today has a different value to you than getting $100 somewhere in the future. So to know whether a deal is interesting, I do not just have to know how much I will be getting back in return for my investment, but when. Getting back $180 as a single lump sum payment in a year is different than getting 12 monthly payments of $15 each month for the next year, even though in both cases you will have payed me back $180 looking back.
The interest rate the bank quotes, in your example 2%, is the percentage amount by which your outstanding IOU to them will be increased at the end of the month, before you make your monthly payment.
Now this was an example of a simple fixed interest rate. In practice there are unlimited kinds of formulas that can have variable interest rates over time tied too other things, capped or uncapped, and even then that is just one of the things that goes into a payments plan. So unless you have nailed down all the other factors, comparing just interest percentage A with interest percentage B, typically in the final haggle, tells you little.
This is why I advice always looking at the series of monthly payments that you will have to make over the duration of the loan repayment, and compare these with the series of monthly payments due under a competing proposal.
Banks will screw you over in more ways than you can imagine, but quoting a compound interest rate as opposed to a total amount repaid at the end of contract (which btw is often much longer than the repayment period or even unlimited in time but that is another story) isn't where it is at.
The thing about loans is that they should also be cheaper if you pay them off sooner. I could believe that they should be simple interest instead of compound, but that’ll get to 200% in only a bit longer (50 periods of 2% interest instead of 35), and banks would want higher interest rates on simple interest anyway, making it equal out. Plus, there are many great loan calculators online to use too.
That's what the 'A' in APR means. It's pretty clear.
If I take out a £100000 loan with an APR of 2% and pay it back in full at the end of the first year, then the total amount I pay back is £102000. Apart from any early repayment charges, the original total term is irrelevant.
When taking out such a large sum, over such a duration for buying your home, the total amount to repay is not the important aspect. It's not like taking out a loan to buy a car or a holiday. You don't have the option of choosing between buying now with a loan, or saving up for a few more months or years to buy without one.
Affordability of the regular repayments over the duration of the loan is the key thing.
There is absolutely no way I would take out a loan of that size with fixed interest in the way you describe. It would be far too expensive, and give the bank too much power.
I'm relying on the fact that I can make large overpayments in order to own my home outright halfway through the original term. That couldn't happen without an annual interest rate. In fact, the most logical thing to do in that situation is to stretch the loan out for as long as possible, so that inflation makes your repayments cheaper.
For a rough example -
Imagine you bought a house for £100K 5 years ago, the interest is such that over 20 years it will cost £150K total (e.g. 3.5% over 25 years).
You have probably paid about 30K, taking about £15K off the capital.
You sell the house for the same amount you bought it. With annual interest, you owe the bank £85K, you give them that, and use the spare 15K for your next home.
With a fixed price, you still owe the bank £120K. You give them the £100K you got from selling the house, and you somehow have to find £20K to pay them the rest.
This is a good example why one should understand compound interest. Through in a payment schedule and amortization as well.
The bank is giving you $X to buy the house. You’re paying off a piece of it each month (your mortgage payment). Part of that goes to the interest on the loan, the rest goes to principal. The interest each month is based upon on the remaining principal. That means your payment starts off being mostly interest and gradually becomes mostly paying off principal.
You could say, “But I can just save the full price and then buy the house with no interest!”. Sure you could. But you’re forgetting that you’re living in the house (or renting it out...) while you’re paying it off.
"Part of that goes to the interest on the loan, the rest goes to principal."
That's only one kind of mortgage though - for a while there were mortgages available in the UK where you only payed the interest on the principal but you also payed into a separate saving scheme with the idea that when the latter matured it would pay off the former.
No idea if these are still available, but for a while in the early 1990s you used to get a very hard sell on them - we had one for a five years or so. In reality they are a terrible idea as you are paying interest on a non-decreasing principal which is a shockingly bad idea and then there is the risk of the saving scheme performance as well.
Edit: Of course you got a hard sell on them as they were clearly a terrible idea from the borrowers perspective but were far more profitable than a normal mortgage for the lender.
These are still around and pushed pretty heavily, but they are primarily for "Buy to Let" mortgages in my research. And offer an astounding TERRIBLE rate on top of the astoundingly terrible concept.
That said, the interest is a great write off for a landlord, especially if they are personally the originator of the loan to their holding company.
Just seems like a massive scam thats become the norm. You're paying off interest on the first month, as if you've already had the money for 20 years. They take liberties from day one.
Let's break this down with a simple example:
You get a 30yr mortgage for $100,000 at 5%
If you paid $0 on principal your first year, the interest would be $100,000x0.05=$5000
Make it monthly: $5000/12=$416.67 rounded up to $417
On an amortization schedule, the fixed payment is calculated at $537, with $120 going to principal and $417 going to interest on your first payment. Exactly what you would expect to pay. The interest isn't front loaded, it's just the actual accrued interest of what you have borrowed.
When you pay the $120 in principal on your first payment, your debt reduces to $99,880. $99,880x0.05/12=$416 rounded. Therefore, your next payment, still at the fixed rate of $537 is now paying $121 in principal, and $416 in interest.
In short, when you have a large debt, you pay larger interest, when you have a smaller debt, you pay smaller interest. This isn't exploitation, just mathematics.
I conclude that they should just work out the total repayable and be honest and say this is a 70% mortgage. not claim it's 2% but just keep re applying that 2% every month or week or day as they see fit.
Most of the time, the total interest paid is included in the amortization plan. It's also easy to figure out. Using my example, the exact payment was $536.82.
$536.82x12x30=$193,255.20
Total($193,255.20)-Principal($100,000)=TotalInterest($93,255.20) give or take a dollar.
And so according to your desire, you'd want them to say it is a 93% mortgage.
The reason they don't is that interest rates and compounding are typically done annually. You also have the ability to make extra payments sometimes, which can pay it down faster. The faster you pay the debt, the less interest you pay.
For instance, if you win the lotto, receive a life insurance payout, or inheritance, etc and pay off the loan within the first year, it's no longer a 93% mortgage but a 5% one.
To me, it makes more sense to say, you owe $100,000 your first year, or $98,398 your second year, and that you'll be paying 5% interest over that year.
Hey, kudos to you for admitting this! I mean that seriously. There are very few folks who actually try to learn and understand things: it appears that you're one of them.
But that depends entirely upon how long you take to repay it. If you pay the loan aggressively up front, you pay less; if you make minimum payments for as long as possible, you pay more.
It’s 5% per year because you are charged interest on some schedule based on how much you have paid off. 5% is a rate, 93% is a total amount and it only applies if you pay the whole mortgage off at exactly the prescribed rate. Many banks’ mortgage calculators will show you the total amount paid anyway so it’s not like they’re hiding it.
Your point seems to be basically that because you can’t do the maths, the mortgage is misleading. That is maybe a fair argument in some cases with financial products. Investment banks are notorious for obscuring the true cost of deals with complicated maths. However this doesn’t seem like a case of that. If the interest rate is 5% APR and you are free to pay it off as fast or as slowly as you like within some bounds, for example, it is absolutely essential that you understand what a 5% rate means to know how the mortgage works.
edit: not to mention that 5% is already a contrived figure not representative of how the interest is actually applied, designed to make it easier for you to understand what you’re charged. Your interest is probably calculated monthly or daily, not yearly. They could present you a nice hypothetical yearly figure, or a nice just-as-hypothetical 93% three-year figure. What’s the difference? Neither of them are real. Your interest is charged monthly, so they’re equally fake and misleading.
Why should there be no charge for borrrowing the money for 20 years? That doesn’t make sense, you have had the money for 1 month when you make the first payment, and so you are charged for it.
I don't understand this. You have negotiated to pay a fixed payment per month so why does it matter whether the money is paying off interest or the principal first? The bank didn't force you to get the loan.
It matters to the bank. Also, the interest can be written off against income taxes, which helps people more in practical money left over to use when they are earlier in the amortization, and probably their career.
Bank didn't force me. Society has made it virtually impossible for me to own a property without one. Which seems unfair when a lot of people got their property 35 years before I was born for the equivelant of 2 years salary.
If you lend me $X at 3.5%/yr for 30 years and I can earn 7%/yr elsewhere, like by investing in a S&P index tracker. Say there's no minimum payment on your loan, just to keep the math easy. In 30 years, I'm going to owe you 2.8 * X (via 1.035^30). My investment of that $X loan has grown into 7.6 * X (via 1.07^30). After tax, call it 6.5 * X. After I pay you off, I've earned about 3.7 * X.
If the initial loan was $400k on a $500k house, then yeah it sucks that I've payed you $1.1M, a clear overpayment, but I wont be sad because I'm coming out ahead by about $1.5M.
In reality, loans come with minimum payments, so you can't come out quite so far ahead. What this all means is if you can do something better with your money, (e.g. market tracker at 7% on a 3.5% loan), then just pay the minimum and do that better thing with the rest. If you can't (e.g. market tracker at 7% on an 8% loan), then pay it down as fast as you can, or don't take it in the first place unless there are other factors.
Depending on your country, the law may require the bank to actually print the total cost of the loan on the contract as well.
You'd have a better argument with revolving credits, the rates of which are generally much more predatory.
That isn't inflation. Inflation is about consumables. If the valuation of assets rise, that is actually the opposite: If you sell the asset, the returns can buy you more consumables.
And neither S&P nor NASDAQ had anything resembling rampant gains, BTW:
In the last ten years the NASDAQ index went from 2.000 to 8.500 and the S&P500 from 1.000 to over 3.000 in what is generally referred to as the "10 year rally".
Inflation as in the rise in price of a basket of goods is generally used in reference to the consumer price index, but can also be used in reference to stocks, and baskets of those such as the indices.
And before S&P went from 400 to 7000 largely uninterrupted, and NASDAQ from 350 to 7100. But as those are compounding values (i.e. there is not a linear realationship between year n and year n+1, but an exponential one) one can gain more insights from comparisons of the annual returns - that is the reason why I linked those. The annual returns are not unusual, though. Please have a look at them!
If the prices of assets rise, that is appreciation. If stocks or houses appreciate, you can sell them and profit: Your purchasing power rises. If consumables experience inflation, you can not sell them for a profit: They are either immaterial, like services, or can rot, like food. This isn't pedantry, these are different concepts.
Compound interest is probably the most powerful "force" governing out lives.
It is crucial when borrowing money, especially for longer terms.
It is crucial when saving and investing.
It is crucial in self-development, where a tiny 5% improvement in some area of your life per year can mean that you are twice as good at something in 15 years.
It is important when evaluating any kinds of improvements in personal life or in business.
The trick is that the percentage never sounds like much. The number of years always sounds like a lot. Nonetheless, the years WILL pass whether you want them to or not, and what tiny life choices you make throughout have a huge impact on where you will be in the future.
Being aware of that does not take much. An hour of intense concentration should be enough to get this insight. Of course, this depends on your age and math background. However, I feel confident saying the above as this to the Hacker News audience, as the above requires nothing more than an imagination and the ability to add and multiply by decimals.