7 Simple Calculations that Show the Awesome Power of Compound Interest

hey everybody welcome back to the financial freedom show my name is rob berger in today's video we're going to look at compound interest it really is our superpower when it comes to building wealth and so what we're going to do is walk through seven really simple uh compound interest calculations that will just demonstrate the awesome power of compounding and i'm also going to show you a very simple compound interest calculator that i built in google sheets and at the end of the video i'll show you how you can get access to it so you can run your own numbers now as we get started i want to make sure we're on the same page when it comes to compounding so compound interest or compounding is simply just earning uh money not only on the amounts that you've invested but also on the amounts that those investments have earned sometimes you'll hear referred to as interest on interest or earnings on earnings so in a simple example would be a savings account and you invest say a thousand dollars it earns it uh interested in today's rates it wouldn't earn much but it earns some interest that gets added to your account and then the next time uh the interest accumulates it accumulates not only on your original one thousand dollar principle but also on the interest you earned the last time and that just repeats over and over and over again same thing happens with a bond or bond fund where it generates interest and you reinvest it and it continues to grow or with stocks and with stocks or stock funds they actually kind of compound in in two ways if you have a fund or an individual stock that pays a dividend compounding occurs when you take that dividend and reinvest it but one thing that's nice about stocks is even if a company doesn't pay a dividend they still compound and that may be a little hard to believe but think about companies like alphabet which owns google or tesla or amazon or berkshire hathaway these are companies that at least at the moment don't pay a dividend but they earn a lot of money they have profit cash flows and they take that money and what do they do with it well they don't pay a dividend to shareholders like you and me but they reinvest that money back into the business to do more research and development come up with more products and services and that's where the compounding occurs now keep in mind there are some things that don't really compound at least not in the way that we're talking today think bitcoin or gold they in and of themselves don't earn anything they just sit there that doesn't mean you can't make a lot of money we all know uh cryptocurrencies have made some people extremely wealthy but these things don't compound in the way we're talking about because they're not an asset then in and of itself earns uh anything so with that in mind here's what we're going to do i'm going to show you the compound calculator that we're going to use today and in fact here it is and i'll uh oops there we go and here's what we're going to do as a baseline let's let's assume that compounding didn't exist that we couldn't compound our returns and here's the assumptions we're going to use and this is the calculator i'll give you access to in in just a minute we're going to assume an annual income of fifty thousand dollars this is for someone either right out of high school or college and yes you're saying wait a minute someone out of high school pie doesn't make that much well you're quite quite right most don't i certainly didn't but here's what we're gonna do we're gonna assume that this person never ever gets a raise they work 45 years and they never get a raise and we're also going to make it hard on them we're going to assume they can never save more than 5 percent that goes right here so most they can save which comes out as you can see dollars and 33 cents and by the way some of these are red indicating that we don't have to input anything there they're calculated values and i'll explain what these numbers are uh in just a bit uh the green boxes are what we populate and in fact some of these let me just quickly delete as we go let's make it a bit easier and so we're going to assume uh five percent that's the most you can save and at the moment we're gonna assume no compounding you actually a zero percent return how's that that's not too good but there you go and we're going to do 45 years this is sort of a typical traditional working period say from 20 to 65 or 22 to 67 and if we did that we'll ignore this number for a moment you can see uh well we have a hundred and twelve thousand five hundred dollars that's what we've saved uh over a 45-year period assuming a fifty thousand dollar uh annual salary and a savings rate of five percent we haven't earned anything we've effectively stuffed this money under our mattress there it is a hundred and twelve thousand five hundred now i i show you this uh somewhat silly example so that we can really begin to see the real power of compounding and that gets us to our very first of seven calculations and all i'm going to do is add a return number here we're going to assume we invest it maybe in a simple low-cost index fund portfolio and i'm going to assume a return of 9.8 percent and you may say well where'd that number come from well it came from vanguard as you can see on the screen uh a 80 20 portfolio from 1926 to 2020 has an average annual return of nine point eight percent again uh when you get access to the spreadsheet you can assume whatever returns you want but uh i'm just gonna use vanguard's number and we'll put it in here 9.8 and uh bam there it is uh to over two million dollars and this really if there's if there's no other takeaways from this video this is really the power so think about this the 112 500 is from saving that's from you know spending less than you make maybe making some sacrifices putting money aside we turned that into two million dollars what did we do well we simply invested the money in frankly low-cost index funds during our working years we didn't work overtime to generate that we didn't get a second or third job we didn't cut back uh even more and we made all of this while we were sleeping while we were on vacation it was very very little effort the 112 500 that's the effort right spending less than you make but it turns into a pile of cash if and this is a big if we give it enough time and so that's the real power of compounding now i want to sort of start to peel back the the the layers on this just a bit to show you just how important uh some of these numbers are so you notice we're saving for 45 years well what would happen if we just save for 44. so i'm going to make some changes to this calculator i'm going to bring this number down and put it here there's the formula don't really have to worry about that but what i'm going to do is this number right here is what we use for the time period and so what i'm going to do is just just shave off one year what would one year matter instead of 45 years we'll save for 44 years well it matters a lot in fact we can see what the difference is by simply taking this number and subtracting this number by reducing our savings period from 45 years just to 44 just a one year difference we lost almost 200 000 dollars by the time we retired yes every year matters which is why i stress that i believe everyone should be investing today even if you can only afford to invest a few bucks a month now that gets me to the third uh the third calculation and i'm going to pick on dave ramsey a bit here he's great at getting out of debt but one of the things he believes is that you should not invest until you've paid off all of your non-mortgage debt and it's a it's a view that i just i disagree with and so for this third calculation let's imagine that someone followed that approach and it took them we're going to assume seven years to pay off all of their low interest student loans and so they didn't invest for 45 years they ended up investing for 38. well that decision cost them by the time they retired over a million dollars the numbers get silly big when you're talking about long periods of time and shaving off those seven years because it's those those last years where the compounding really kicks into overdrive all right and so delaying uh investing even relatively short periods of time will have a huge impact on the final outcome all right now the other factors matter too so let's take this away for just a minute and we'll take this away and now i'm going to copy this back over and what i want to do now is make a different assumption we're going to keep it at 45 years but you notice i put 9.8 here so in this formula here we're going to change that 9.8 this is the number here and we're going to change it just one-tenth of one percent that's it 9.7 well if we do that well we get a number that i wasn't expecting let me try that again i see what i did we'll do 9.7 there we go and again we can compare these two numbers just one tenth of one percent cost us 70 grand and uh so not not a big difference in the returns and a significant difference in the number now it might not be life-changing but personally i'd rather have the 70 grand than not but the reason i show you this is we can't control what the stock market will do so you know i've assumed 9.8 over here that's this number here this number is 9.7 we don't know what the returns are going to be over the next 45 years but it brings me that calculation which was our fourth brings me to the fifth calculation and there is something we can control fees a standard fee from a fiduciary this is someone who's supposed to have your best interests at heart a standard fee is one percent so if returns were 9.8 but they they took one percent off the top that would give us 8.8 returns on an after fee basis yeah big numbers you can see it cost us 600 that that seemingly small one percent uh fee makes a big big uh difference all right uh that gets us to the sixth calculation we've got two more the sixth one is super important you notice we've assumed a five percent savings rate obviously if we work hard we can maybe increase that but what about if we have an employer that matches some of our contributions and so what i want to assume for this calculation right here actually you know what i'll do to make this a little better i'm going to move this down here um and then we're going to change this instead of an of a five percent uh savings rate we're going to assume that they match up to three percent of our salary so it turns into an eight percent and actually just to make this clear i'm going to pull this out for just a second so all we're going to do is we're going to increase our savings rate from five to eight percent but that extra three percent we're assuming that your employer matches your contribution so remember this number is two million we'll round it down it's two million thirty five thousand but let's call it two million what happens if we make this eight percent look at that it went from roughly two million dollars to 3.2 million dollars a huge difference now of course we could have created this on our own without an employer match but it would have required some more sacrifice it would have increased our monthly savings from remember it was 208 dollars a month to now 333 but with an employer match and again i know not everyone has an employer match but if you do that employer match is incredibly incredibly valuable by the way it's just another reason why i don't think we should hold off saving even to pay off other debt particularly if our employer matches our 401k contributions i mean that's just losing free money we've got to take advantage of that all right all right let's move to the the seventh and final calculation this one's really important we're going to put the savings rate back to 5 and we're going to make some changes here and i'm going to actually change some of the calculators a bit to do this but the first thing i want to assume is that we only save for 10 years now look at that number uh 42 000. you know we were looking at millions and now you know 10 years still seems like a long time but we've only got 42 grand that might be a bit disappointing and it is something that that's worth noting the benefits of compounding take time uh it's slow at first most of what you have in the first few years even the first decade is largely uh what you've saved yes there's compounding taking place but it's very small numbers in fact let me show you this uh compound interest calculator from investor.gov i'll leave a link to this below the video here we're assuming a monthly contribution of 250. let me try to make this a little bigger for you nope that's as big as it'll get but here's what i want to show you 45 years here i assumed an 8 interest rate but here's the key takeaway it's this uh chart at the bottom the red shows our total value which of course includes compounding this greenish line shows just our contributions and you'll notice for about the first 10 years those lines are almost indistinguishable they're right on top of each other they don't really start to separate until around year 10 or 12 or even close to 14 right here and that's something to keep in mind compounding takes time but once you get it going the results are amazing and that brings us back to this seventh calculation i want to show you i want to assume that someone saves 208 dollars a month for 10 years at 9.8 percent intra return and then they stop they don't save another thing but they keep this 42 000 invested for another 35 years so how would we do that well we can do this formula this is the same formula that drives the numbers up here it's just a future value formula and we're going to give it an interest rate that same 9.8 percent we'll divide it by 12 uh to make it uh a monthly right and this is going to be for 35 years so 35 times 12 because we're keeping things monthly we're not going to contribute another nickel so that will be zero but we're not starting at zero right we've got that 42 191 i'm going to make that a negative number what do we end up with well we end up with 1.2 million dollars still a nice nest egg even though we only saved for 10 years and let it let it grow for 35 years why have i done this well i want to compare this to someone who doesn't save their first 10 years they wait 10 years maybe till their early 30s and then they start saving and they save for 35 years what would that look like well we'll use the same return divided by 12. we're going to save for 35 years and we're going to save that same 208 33 what do they end up with 751 000 and they have contributed a lot more money right because they've contributed we can calculate this 208 well we could just use this they've contributed 283 per month for 35 years 87 000. this person who started early what did they contribute well they contributed 208 a month as well but they only contributed for 10 years 25 000 versus 87 500 but their number it's not quite twice as much but boy it's close and why it's because they started earlier 10 years earlier and even though they contributed less their money had a much much longer period of time to grow so there you go those are the seven calculations i hope they show you the awesome power of compounding it really is what will build wealth for us now i promised you i'd give you access to the spreadsheet so you can run your own numbers so here's the thing i'm going to leave a link to this spreadsheet below the video please do not click the share button instead go to file and make a copy you can make your own copy only you will have access to it and you can change these numbers and run whatever scenarios you'd like to well listen i hope this has been helpful to you if you have any questions leave them in the comments below be happy to help you out any way i can and until next time remember the best thing money can buy is financial freedom

Channel: Rob Berger

Views: 53,961

Keywords: compound interest, compound interest formula, compound interest explained, compounding interest, compound interest investment, compound interest and simple interest, compound interest stocks, compound interest calculator, compound interest investment options, compound interest investment in stocks, compound interest investment calculator, compounding interest investments, compounding interest calculator, compounding interest stocks

Id: _GhNO7knSRE

Length: 17min 13sec (1033 seconds)

Published: Tue Nov 09 2021