24 Oct 2015, 3:28pm
personal finance
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  • Compound Interest – quantitative takedown

    I keep getting flack for being cynical on compound interest. I was an engineer in a previous life, and this is amenable to quantitative analysis, here are the charts on why compound interest won’t help you that much to retire early. It will help you a bit. but if you want it to do the lion’s share then be prepared for a nice 40 or 50 year working life.

    You know the story of Alice in a Wonderland of Compound Interest. Astute Alice saves £1000 a year from 18 to 38. She then stops work to have children, never saves any more in her pension and retires at 68 on £1M. Lovely jubbly. Cat-brained Camilla jumps to it at 38, and saves £1000 for 30 years until 68 but lives on cat food and baked beans for the rest of her life.

    Let’s test this for Sensible Susan who works for 40 years from 21 to 61. Nobody in the personal finance field wants to work for 50 years like Alice 🙂 Warren Buffett tells us that she should expect an annual real return of about 5%. She works in the public sector and never gets any real career progression. To normalise everything I have her saving one unit of real money every year, all these entities live in an inflationless world where their nominal rate of return on capital is deflated by inflation to get the real return. At the end of her career she looks back at how much each tenth of her working life has contributed to her pension. Compound interest sees to it that the early years contribute more, that much is clear, and of the total amount of 120 units accumulated, 67% is compound interest – it triples her money.

    Amount each tenth of her career (four years to a pie slice) steady savings contribute to Susan’s pension, saving exactly the same amount in real terms for 40 years and at 5% p.a. real return

    She observes that the savings in the first third of her working life contribute half her pension capital, she goes out and tells all the young pups that the first 12 years of savings are the most critical, if she had started at 35 she would be on cat food and beans. Quod erat demonstrandum.

    Let’s cast a beady eye at how this compares with the real world:

    Susan got no career progression. Let us hear it from the people at the ONS on this subject. The downturn is because everyone took the earnings sucker punch from the financial crisis, I correspond roughly to line 2. Look at how the career paths of people 10 years younger than me leave my cohort for dust 1 😉

    career progression is much faster now

    I got roughly three times real terms career progression over 30 years, this happens faster now though it may peak earlier, and I did better than the ONS average. It’s not unreasonable to expect someone to save to a pension as a constant proportion of their gross salary. Let’s say Susan got 2 times real terms career progression over 40 years – compound interest still more than doubles her money, it’s 63% of the total of 164 units

    Susan saves a steady segment of salary as it doubles in real terms

    Susan saves a steady segment of salary as it doubles in real terms

    Just for the record, this is what this would have looked like for me, getting 3x career progression although that was in 30, not 40 years so I have just taken eight of Susan’s four-year segments, getting 3x career progression over that 32 year time. 52% of my total of 134 units comes from compound interest – it’s doing a hell of a lot less of the lifting than for flatline Susan. But I end up with more 😉

    three times career progression in 32 simulated years - the pies are eighths, not tenths in this chart

    three times career progression in 32 simulated years – the pies are eighths, not tenths in this chart. The pies are more even than Susan’s

    It is the combination of career progression and the shortened working life of FI/RE types that makes compounding a lot less relevant in the real world. I’m not even particularly exceptional here – a 30 year working life is early retirement, not the extreme early retirement, and I dramatically lacked ambition compared to what people like RIT or The Escape Artist were prepared to do to retire early. I would imagine they got more than three times real terms career progression.

    Even that’s not realistic, though. There is a problem in humans called hyperbolic discounting, which means when we are closer to something delivering it gets much more interesting. The young Ermine didn’t really bother about pensions, though of course I signed up the The Firm’s scheme – companies were more paternalistic in those days and told you what was good for you. As the concept of retirement hove into view and I got within ten years of NRA I started to divide the tax privilege of 40% by the number of years (10) and saw I would struggle to get that sort of return on cash, and all of a sudden AVCs (a DC type of pension saving) became interesting, so I set to it. Tax savings mean a HRT taxpayer gets a 66% return on net income foregone, compared to the 25% for a basic rate taxpayer. I was lucky enough to be able to save to AVCs by salary sacrifice, so I took some basic rate tax + NI savings which still worked out to about a 50% ROI. The whole thing gets a hell of a lot more interesting. I don’t know about you, but it really, seriously, pissed me right off to be working two days a week for the taxman to I tried everything legit as I started running into HRT – first employee share incentive plan shares, and then somebody introduced me to AVCs and life was sweet. Life is too short to work nearly half for the government 2, a third is okay, more than that, sod that.

    I tried to simulate the effect of that by increasing the Ermine’s later savings by 1.3 times, which reflects the better return on net earnings lost that a HRT taxpayer gets. It somewhat underestimates my later savings, I was simply not prepared to pay 40% tax at all after a bit, so any bonuses and pay increases were salary sacrificed to AVCs and in the very last two years I hit AVCs harder driving my pay well below the HRT threshold. But ignoring that and simulating my boosted contributions from HRT alone, the contribution to my savings if I had saved steadily as a proportion of net income is much more even across the eighths of my career –

    Add HRT boosts into the mix a way into the career plus career progression and compound interest is beaten out by bigger contributions later

    Add HRT boosts into the mix a way into the career plus career progression and compound interest is beaten out by bigger contributions later

    Compound interest is about half the total 145 units. Unlike for the slow savers it just doesn’t do much for aggressive savers, and I was never a particularly aggressive saver compared to the people who want to retire in their forties!

    There’s a takeaway from this all – yes, compound interest will help you triple your savings to FI, if you are unambitious and you want to work 40 or 50 years. It will roughly double the savings of the typical FI/RE saver. Where it really starts to show up is once you have FI and your aggregate savings are significant. Some anonymous dude called Cumulative Dividends has put more money into my ISA 3 than I have this year. He appears to be gathering speed with time – in the last tax year he contributed nearly a fifth of what I did. He is one aspect of compounding, there is a similar but volatile and flighty bastard called Capital Appreciation that is the other.

    I will not be drawing down my ISA savings for probably another 10-15 years until my final salary pension starts to be eroded relative to other people’s earnings (earnings inflation is usually higher than price inflation) and then I will start to use the tax-free ISA income to top my pension up, and finally start to run the capital down or part-buy an annuity in 20 years’ time. Who knows. Compound interest helps people with capital, but it doesn’t help ambitious early retirement savers to build capital that much, though it roughly doubles the money. As for Alice in compound interest wonderland, well that is Alice in Wonderland – the weakness of that is the unrealistic 10% annual real return. Alice may get that in Wonderland, but you ain’t gonna get that in the real world. Put the work in or put the time in.

    You shouldn’t take away from this that you don’t need to start saving to a pension early, all the parts of the pie matter, but you shouldn’t take it as totally devastating if you didn’t start early. If you have any ambition to early retirement at all, the myth of compound interest and the trickle of free money from Time isn’t going to do the heavy lifting for you in the accumulation phase.

     

     

    Notes:

    1. I acknowledge they need that better career progression, to be able to pay for student loans if applicable and housing which is dearer in real terms than back in the day. It’s still an impressive feat and I tip my hat to their superior industry or negotiating power, at least up until ’09
    2. I know, indirect taxes and Tax Freedom Day and all that, you can reduce indirect taxes by not buying loads of Consumer Shit
    3. over its ~six year existence

    Hi ermine

    I never normally link to blog posts that I’ve personally written (and please delete if inappropriate) but the 3rd chart in this post http://www.retirementinvestingtoday.com/2015/10/a-retirement-investing-today-9-months.html might help with the discussion/debate by detailing my personal experience of this. I’ve found that my FIRE journey has been all about saving rather than compound interest. Sure it’s helped but in every year bar one my savings have increased my wealth more than investment return. It’s also not just because I’m early into my journey as I now have 85% of the total wealth I need and it’s still occurring.

    Cheers
    RIT

    Your insight is welcome – any time 🙂 FIRE journeys are time-telescoped by definition, it surprised me just how much difference the 40 year timescale was different to the 30-year one.Your 8 years if saving is a timescale where CI won’t get out of the starting blocks. Whereas your 50/60 year retirement is where it will show!

    OK, how about this model, which I am going to call “semi-extreme-semi-early-retirement”:
    – graduate at age 22, get rapid promotions early in career but keep your cost of living reasonable so you have a high savings rate
    – keep saving a very high proportion of wages until some point around age 47 when you get forced out or can’t take it any more
    – freeze your accrued ISA and pension balances and let them compound for another 10 years or so to bridge the gap to full retirement
    – spend those interim years doing something more interesting or at least tolerable, a paid job or self-employed opportunity which pays enough to cover the bills but doesn’t need to give you much spare cash to save

    In this situation you have 25 years of well paid career followed by 10 years of winding down and not getting too stressed. Compounding works on your savings for between 10 and 35 years.

    This is starting to become my unofficial plan because I can’t see myself carrying on in a high pressure environment indefinitely, but like the vast majority of people (ermines excluded) I also can’t see myself earning nothing at all once I quit the rat race relatively early.

    I’m not sure how the maths of all this adds up. I suspect the main challenges now are graduate debt and expensive housing, but I can’t accept they’re total showstoppers and if people want to do this I think they’ll find a way.

    It’s a good one – it works well with the debt dynamics of graduate debt (you don’t repay if you earn a low amount, and it gets written off after a while, don’t know if pension comes off first)

    It may become a more common model with those jobs that pay well but burn people out in mid-career. It’s not quite Keynes’ Economic Possibilities for our Grandchildren, but it’s a step that way!

    David,your scenario is exactly how things played out for me.

    Sums only work because of house price inflation and generous tax relief on 50k a year SIPP contributions. Some sacrifice but mostly good luck. Plus a well timed redundancy. If tax relief is cut and you can’t do much but pay of a mortgage and a student loan I can’t see how it will be possible for many.

    Hi Ermine

    Don’t you just love that Cumulative Dividends guy, I am also loving Annual Dividends guy coz he will give me over £6,000 this year, and will probably be even more generous next year.

    Surely the benefit of dividends re-invested is Compound Interest?

    I do agree though that the true benefit of CI is when a any two of the three elements (time, return, starting value) are significant, the problem for most of us is that the starting value is not so significant as we are saving from a small salary when we are younger, and if you want to retire extremely early the time element is not so significant either.

    On the other end of your working life you may have a significant savings amount, but the time is shorter still.

    If you can manage to reach retirement and live on less than the income you receive from investing, if you have retired early this is when the CI will start to accumulate.

    Best Wishes

    > Surely the benefit of dividends re-invested is Compound Interest?

    That’s the part where it may help you afterwards IMO 🙂 The trouble is for that to make a decent difference you have to have a fair whack accumulated – I’m definitely of the feeling CI helps you when you’ve arrived. Just not so much to get there, particularly if you get improvements in pay along the line

    For a FIRE considering a 40 year retirement, then compounding is helping them, as for the first 10 years provided the fund outperforms the withdrawal rate, those savings are compounded to benefit the last 10 years.

    People often consider accumulation and withdrawal phases with the switch at retirement, and argue a switch from equity to bonds at the end of the first phase to avoid risk, but for FIRE the internally-funded accumulation trajectory needs to continue for a decade more, to ensure realistic funds at more normal retirement ages, so you need to keep in equity.

    When I pull the trigger soon, I expect the real returns on my savings to be equivalent to a decent salary, only with a better tax position with ISA/pension havens and no NI to give that excess.

    > People often consider accumulation and withdrawal phases with the switch at retirement, and argue a switch from equity to bonds at the end of the first phase to avoid risk

    Wasn’t this for the recent historical case where you had to crystallise the fund to buy an annuity – effectively suddenly changing the fund into something very 100% bond-like? I certainly agree it would be a strange thing to do in the new pensions world for the reasons you say – a retirement could be 30,40 years and it would be a strange thing to reduce the compounding at the high-water mark of one’s accumulated savings by switching asset class that early!

    There may be a case for a gradual derisking later on – I may consider buying an annuity or a time-spaced ladder of them should I get to 75-80 or so.

    The thing is the whole of the defined contribution pension concept relies on the compound interest theory…if that doesn’t work then there is nothing to pay for retirement

    Be interesting to see how that one plays out in the next decade…particularly when the stockmarket crashes again…as it will

    I’d be the first to acknowledge my good fortune in getting what turned out to be more pay than they anticipated 😉 Most of the issue is that the great stories told about compound interest helping accumulation are only valid for long working lives – much longer than the FI/RE community’s aim of 20-25 years and indeed longer than my 30 – the Telegraph’s illustration has a working life of 50 years! It’s a very slow train in the accumulation phase IMO.

    26 Oct 2015, 12:51pm
    by raymac1946

    reply

    @ermine I was 21 in 1967 and I am pretty sure my career choices did not result in all that much of a salary progression. What I did have was a wife who worked all that time and had a great DB pension at the end.
    Also we benefited from relatively low real estate costs even though interest rates were high for a good portion of our mortgage indemnity. Our student debt was minimal compared to what kids face today.
    We are where we are today because of saving as much of one salary as we could while paying the bills with the other. We had 33 & 35 year working lives and considered ourselves lucky to get out 7-10 years ahead of time.

    A lower career progression is coherent with historical changes – you, and I, worked through far less dynamic times, I have to say I am amazed at the ONS’s chart of career progression, and this is the median chart. It’s quite amazing – the median Brit gets the sort of career progression it took me 30 years to achieve in half the time. These are presumably the people who gain from the increasing speed of change and range of opportunities. If we look further back in time to before the war progression seems much slower, and capital built much slower than now.

    But as you say, housing and student debt is much more in real terms now which will take a bite out of that. Whether it’s cause or effect is hard to say – that rapid increase in median pay is probably lifted in the UK by the finance industry, I don’t think everybody experiences that sort of progression. They can pay the excess, but this forces everybody else to bid higher for some common goods – which is why most of the families of people i went to school with wouldn’t be able to afford to live in London on the pay from that sort of job nowadays

    Hi Ermine,
    Good post. Good to see how you break up the consistent opinions out in the PF world. I prefer the realistic tone your blog brings to the mix.

    I agree for ERE, compound interest may do little in the grand scheme of things. However I think you assume all of retirement money is one big pot which isn’t always the case. As early retirement can be a big goal, I broke it down and prioritised. By prioritizing the long term goal first, compound interest has allowed us to put less money there and focus on the short term goal.

    My partner and I have had sound financial sense that we invested in the pension pot early. We have at least four SIPP/pensions between us, that we can’t tap until the magic age of Age 67 (or 70). As we’re fairly young, we can’t touch that money for another 30/35 years or so anyway, so compound interest is useful there. Because we’ve done a good job, we realised even if we stopped adding money it would grow to a size where we can’t spend it all.

    This analysis allows us to strategize to focus on retirement pot 2; AKA early retirement from Age X – 67 which is best funded through ISA account. In this pot, compound interest makes less sense. Without the impeding doom of “Will my money last forever”, I only have to make the money last until I’m 67. This gives me an absolute floor. £AAA to stop working forever and never have to take in another paycheck, £BBB I can choose to cut back on the hours, or go freelance. I can start making tradeoffs with current lifestyle and finances.

    Of course I don’t want to be desperate and wait for the day I turn 67, but it gives me more freedom and wiggle room to think outside of the box for early retirement.

    Keep up the good work.

    Interesting post, and a good dissection of the different roles interest compounding plays at different life stages, or perhaps portfolio value is more appropriate way to look at it. I had a similar experinece to ermine and many others I guess – didn’t take much notice of pensions and savings other than being in the employer’s scheme until later in my careeer path when I started to feel the need to have options other than plodding along until I had one foot in the grave. Strangely I more or less stumbled into doing the right thing through having an interst only mortgage that I had to take out when I had to start home buying a secong time round after divorce. It seemed the only way to afford decent house with the level of payments I could afford, but came with the need to set up an alternative self-funded saving vehicle and offered the prospect of maybe making a little extra on the savings than needed to pay back the principal,.As it happens I recently took my bow from full time career employement 5 years early – so nothing like most FIRE enthusiasts plan, but still early enough to raise disbelieving eyebrows among collegues. In the final few years though I belatedly realised the potential benefits of the personal pension fund I’d built up, and started to save much more. My DB scheme pension lump sum paid off the mortgage, it turned out, and I have a personal pension I can continue to sit on and potentially add to.

    So I agree with you ermine that it is the later career stages when you have the wiggle room in terms of earnings and also the motivation and insight to get ones head around saving and investing on a significant scale, by which time interest compounding is largely irrelevant as that bus has trundled off into the mists. However, as you then point out it is once you have accumulated your stash and are relying on it for an indefinite and hopefully multi- decade period when compounding is key.

    What I’d wondered having read your piece, though, was whether it might be helpful to people at the start of their saving and investment careers to think of interest compounding from a different perspective. I was reminded of the charts you provided a while back on the topic of compounding – the stripey ones (if I am right thinking it was in your blog I saw this example…) that show what each year contibutes to the whole in the final portfolio. Your point in that argument was the same as here – the early years savings are small, but compounding gives them impact later on, whereas the later years have relatively much larger contributions but lack time for compounding, so they even out, more or less. So, what if we were to think of the effect of compounding ‘backwards’ when we start investing? These days young people really can reasonably expect to live to near 100, especially women, so if we are just 30 why not start out with the ambition in year 1 to save for our 99th year? To provide an income of 30k in the 99th year, high compared to what most people aim for, a 5% real return over 70 years needs about £82 a month to be invested in year 1 (if I’ve done my sums right…). You could almost think of it like a series of seperate accounts, each filled up in order from your last year back to the present year. You then get to retire when the downward descending ‘account series’ meets the last year you need to save for. I like this idea because you could imagine having a programme that had all the pots you needed to fill, you stick in your current portfolio value, then it back fills them on various scenarios. Early savers would get motivation from easily ticking off the latter years rapidly, as there is no reason why most people couldn’t easily do two or three ‘years’ at a time at the earliest stage, especially once employment pension contributions are factored in, and by the time filling the ‘year accounts’ started to get more difficult young investors would hopefully have got the insight into the nature of the savings demands needed to achieve their saving and retirement goals in the later stages, not to mention more cash from career income growth to satify the demand. For later stage savers this perspective also might provide insight into the tricky issues of ‘can I retire yet’ or ‘do I have enough to retire’. And it also provides insight into how crucial tiny advantages in return are too – if the real return is only 4% your 99th year needs £160 a month to be stashed away when you are 30 – twice as much! Hopefully that is pessimistic for a 70 year view, but it shows you must drive fees down and bump up the commitment to equities, and even fractions of a percentage point gleaned are valuable.

    One of the interesting things your post brings up for me is the greatly added value that the employer match gives at the start, if you can get it. Many people ignore that and lose out on it at the start, what with other things getting in the way. And yet if you anticipate a 30 year working life, over which together with say a doubling due to CI buys you a year of retirement income at the other end, then taking a match gets you two years.

    But that’s because an employer match is a 100% ROI – there aren’t many places you can go and get that 😉

    Nice pie charts! 🙂

    Hmm, so the grand takedown of how we’re over-egging compound interest is that it is:

    — A huge contributor to average workers who plod away for 50 years (the State retirement age is headed towards 70, remember, so in reality this is most people)

    — Still contributes half of all the savings of an aggressive saver / early retirement type

    — Doesn’t contribute much if you only really save for ten years, which shouldn’t shock anybody, least of all a mathematically inclined fellow like you Ermine, because, er, it’s compound interest, which we all know takes time. 🙂

    I think the weasel doth protest too much.

    I appreciate we’re Batman and The Joker on this, will leave you to decide which role you prefer. 🙂

    All the best

    T.I.

    p.s. Will link you up again. All good debate, in mutual good spirit I hope. 🙂

    Perhaps the differing angle is because of the timescales needed, I just don’t think humans live long enough to get compound interest to do most of the heavy lifting. 50 years, 50 flippin’ years – life is too short to spend that long at work! I am long in the tooth, but I’d have had to start down t’mines at 5 to have got 50 years of working. Maybe I am more of a ornery refusenik than most, but it’s a very long part of one’s life. I do take the point that perhaps my working life was a little shorter than average, but that’s a lot of time to be putting in. And my 30-year working life is long compared to many PF writers’ aims.

    I appreciate the disagreement – and indeed it is perhaps because I am looking from the end of the journey looking back. I ain’t got another 20 years of serving The Man in me – I’d kill the blighter first, the way the workplace is going 😉

    — Still contributes half of all the savings of an aggressive saver / early retirement type

    I confess this slightly surprised me – over 30 years and ignoring sequence of returns. It would be interesting to know what the spread of a Monto Carlo run on that were, all the while remembering that stock market returns don’t obey the central limit theorem which makes them more likely to extreme values than normal.

    Those targeting a shorter working life, which will typically be people in finance and to a lesser extent IT who experience that much higher career progression but burnout in their 30s to 40s are on their own, however.

    It’s fair enough to say that if you’re going to work 30 years or more you will appreciate having compounding riding shotgun, but you’re going to be close to carking it if you want compounding to do most of the work. TANSTAAFL etc…

    I think ermine that your view on this is highly influenced, perhaps unconsciously, by your own very specific experience. For me, even on your numbers, compounding (which is really simply the effect of leaving investments alone, reinvesting any payouts, over a long period of time) looks like a pretty important element of amassing enough of a nest egg to fund retirement. clearly, in a low return environment, investments will grown more slowly. But in your particular circumstances, where you turbocharged your investing just as the stock market hit its lowest point and steepest bounce back for decades, I guess the effect of upping your savings rate at just the right time to catch that wave makes everything else look insignificant. As well as that, I assume all your pensions savings at the beginning of your career were into a DB scheme – I think if you’d actually been investing in a DC pot from the get go, you might feel a bit differently.

    There’s no doubt something in what you say, though bear in mind that I saved roughly a third but less than a half of my total pension savings in that last three years (and the bulk of my total capitalisation is in a DB scheme).

    There aren’t that many steady DC savers who started work from the 1980s reporting how it went, because presumably many of them have yet to retire, and also many have savings in the State earning-related pension scheme or whatever SERPS has become, which is a different type of DB system I believe.

    The issue I take with the way compound interest is presented is that it is necessary on those pitifully small early contributions, and weighs less on the later ones after you’ve experienced career progression, which seems much faster now than it was in the past. That fats progression sits ill with a lot of the commentary on the world of work now, but that’s what the ONS stats seems to indicate.

    If anything the message to young people starting out is for God’s sake take as much employer match as you can if it’s on offer – unlike compounding that may or may not be as rapid as in the last 30 years that is a guaranteed win.

    1 Nov 2015, 9:56pm
    by Spud Potatoes

    reply

    Interesting discourse between yourself and The Investor. The Investor’s argument holds true in a theorists world where “everything holds constant” and “in the long run”. Unfortunately life is nowhere near as neat and tidy as one would like, and the truth is that we’re all trapped in the volatile “short term” world. Not forgetting the corrosive effects of inflation in a fiat currency world!

    I’ve actually made the same hidden assumption as TI regarding the currency in taking the ‘real’ return, but I still think the presentation of CI is overegged – the ability to save varies across the life cycle. It would be interesting to simulate the volatitlity in returns and how that affects outcome. Somebody starting investing in 1970 would have their early returns slaughtered by the oil crisis and their mid returns hurt deeply by the rampant inflation of the later period, I don’t know if the stonking preformance of the markets from 1980 onwards would have saved their tail (assuming they gradually shifted away from equities in the last five years before retiring in 2000 in time for the dotcom crash!)

    […] a lot of time or a lot of money on your side. They ain’t making any more time, which is why compound interest won’t save your ass unless you work till you have one foot in the […]

     

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