Jekyll2019-04-14T08:45:58+00:00https://onfi.co.uk/feed.xmlOn FIA holistic take on financial independence, and how to get there, from a uk-based mid twenty-something.The life-changing magic of compounding2019-04-13T06:10:18+00:002019-04-13T06:10:18+00:00https://onfi.co.uk/maths/2019/04/13/life-changing-magic-compound-interest<h3 id="pencil-dont-let-money-sit-around-but-focus-more-on-saving-in-the-early-days">:pencil: Don’t let money sit around, but focus <em>more</em> on saving in the early days</h3>
<p>There are a few key take-aways from this note:</p>
<ul>
<li>money sat around doing nothing (i.e. sat in your current account) is a bad idea</li>
<li>that’s because of the life-changing magic of compounding; i.e. exponential growth</li>
<li>however, in the early days, just getting money saved is the most important thing you can focus on</li>
<li>if you’re aiming to retire early, accept you’ll miss out on the biggest benefits of compounding</li>
</ul>
<p><br /></p>
<h2 id="one-part-1-compound-interest-101">:one: Part 1: compound interest 101</h2>
<p><code class="highlighter-rouge">What actually is compound interest, and why is it important?</code></p>
<h3 id="we-use-the-word-interest-loosely">We use the word ‘interest’ loosely</h3>
<p>When we talk about interest we usually mean two things:</p>
<ul>
<li>The cost of borrowing. he amount of money a bank pays you for the privilege of using the money you’ve deposited with them. Typically they’ll lend this out to people (mortgages, overdrafts, etc) and give you a cut of the interest they charge on that.</li>
<li>The profit you receive as a shareholder in a business. This can either be a <a href="https://www.investopedia.com/terms/d/dividend.asp">dividend</a> which is a share of the profit that business has made, or the relative rise in the share price when you come to sell.</li>
</ul>
<h3 id="there-are-two-main-types-of-interest">There are two main types of interest</h3>
<p>Interest takes two forms, <code class="highlighter-rouge">compound</code> and <code class="highlighter-rouge">simple</code>. Compound interest pays interest <em>this year</em> on both the amount you’ve saved AND the interest you’ve earned <em>last year</em>. Remember - <strong>compound = interest on interest</strong>. Whereas simple interest only pays interest on the amount you’ve saved, and not the interest from last year - so <strong>simple = no interest on interest</strong>.</p>
<h3 id="get-a-free-70k-with-compound-interest">Get a free £70k with compound interest</h3>
<p>Both are better than no interest, but compound interest is significantly better. This chart shows why.</p>
<iframe width="778.1763413945164" height="536.504" seamless="" frameborder="0" scrolling="no" src="https://docs.google.com/spreadsheets/d/e/2PACX-1vRvEiL3wkLkXr_K55ur9ORXZepSQA8Fs0Dw2ZqwgDxwRbgj0UHyXDQ7AmoduBsILNpdPggXj9wFiW43/pubchart?oid=1775916177&format=interactive"></iframe>
<p>It looks at someone saving £3,600/year - or £300/month - for 30 years, and shows the difference after thirty years with no interest, simple interest and compound interest. I’ve assumed you’ll get 3.5% interest.</p>
<p>If you benefit from compound interest you’ll have earned over £70k in free money, or a <strong>70% boost to your savings.</strong></p>
<h3 id="get-even-more-if-you-can-boost-your-interest-rate">Get even more if you can boost your interest rate</h3>
<p>To illustrate the effects of compounding, here’s a table that shows for any starting balance, with no ongoing investment, how much your money will multiply by after different time periods, depending on the interest rate you get.</p>
<p><img src="/assets/img/compounding/compound-table.png" alt="Compound table" /></p>
<p>For example, if you put an amount of money away for 15 years at 5%, you’ll double your money.</p>
<p><br /></p>
<h2 id="two-part-2-compound-interest-and-fi">:two: Part 2: compound interest and FI</h2>
<p><code class="highlighter-rouge">What does compound interest mean for financial independence?</code></p>
<h3 id="optimise-savings-first-rates-second">Optimise savings first, rates second</h3>
<p>You can’t earn any interest on £0.</p>
<p>So, in the early days of your FIRE journey, it makes sense to spend more of your energy trying to optimise your ability to put away savings each month.</p>
<p>That’s not to say you shouldn’t look to get a return on the money, but you shouldn’t be worrying too much about optimising your asset allocation to push the interest rate from 3.5% to 3.7% if you’re only saving 60% of what you could be, for example.</p>
<p>However, as the gap closes, it becomes more worthwhile.</p>
<p><img src="/assets/img/compounding/ten-year-savings.png" alt="Ten year savings" /></p>
<p>After 10 years, saving £9k/year at 5% only puts you £4k behind if you were saving £10k/year at 3.5%, despite you having saved a whole £10k less. That means the interest rate has given you a free £6k.</p>
<p>This says you’ll always be better off saving more. Although once you’ve got that down, of course it’s still sensible to see if you can push your interest rate higher.</p>
<h3 id="youll-probably-miss-out-on-the-best-days">You’ll probably miss out on the best days</h3>
<iframe width="877.489796962208" height="542.528" seamless="" frameborder="0" scrolling="no" src="https://docs.google.com/spreadsheets/d/e/2PACX-1vRvEiL3wkLkXr_K55ur9ORXZepSQA8Fs0Dw2ZqwgDxwRbgj0UHyXDQ7AmoduBsILNpdPggXj9wFiW43/pubchart?oid=1831857375&format=interactive"></iframe>
<p>What this chart shows is the split of your portfolio that’s the actual money you’ve saved, vs the interest you’ve earned on those savings. It assumes you’re saving £10k/year at 5%.</p>
<p>After 10 years, 20% of your portfolio has come from interest. After 40 years over 2/3rds (67%) of your portfolio is the interest you’ve earned on your savings. That means <strong>you’ve tripled your money.</strong></p>
<p>Sadly, if you’re planning to retire early and start drawing down from this portfolio after, say, 15 years, you’ll be missing out on the true life-changing magic of compounding.</p>
<p>It’s worth bearing in mind, but if you’re able to retire after 15 years with everything you need for a fulfilling life, who <em>really</em> cares about the interest you’ve missed out on?</p>:pencil: Don’t let money sit around, but focus more on saving in the early daysClassical FI2019-03-30T14:10:18+00:002019-03-30T14:10:18+00:00https://onfi.co.uk/maths/2019/03/30/classical-fi<p><code class="highlighter-rouge">Hint: it's all about your savings rate</code></p>
<p><img src="/assets/img/mathematical-side.png" alt="Mathematical Side" /></p>
<h2 id="the-classical-approach-to-financial-independence-fi">The classical approach to financial independence (FI)</h2>
<p>Mr Money Mustache (MMM) popularised the <a href="http://www.mrmoneymustache.com/2012/01/13/the-shockingly-simple-math-behind-early-retirement/">“shockingly simple maths behind retirement”</a> back in 2012, and it’s generally seen as the ‘classical’ way to become financial independent (FI).</p>
<p>Classical FI doesn’t care about ratios between pensions and ISAs, about whether you’re <a href="https://minafi.com/fire-meaning">LeanFI or FatFI</a> (yes, those are apparently things), or what age you’re thinking about retiring. It’s a really simple way to let you know when you can retire.</p>
<p>To quickly recap, financial independence, is a state where you have enough wealth to live on, or assets generating enough income, such that you don’t need to work a “normal job” anymore.</p>
<p>As long as you’re investing your savings, and getting a decent <code class="highlighter-rouge">interest rate</code>, they’ll grow and eventually generate enough returns that you can live off the returns alone. At that point you’re financially independent and can stop working if you want.</p>
<p>The percentage you withdraw every year should be slightly less than the interest you’re earning, known as a <code class="highlighter-rouge">safe withdrawal rate (SWR)</code>, that way the money shouldn’t run out, and you’ve got a little margin for poor performing years.</p>
<h2 id="savings-rate-is-key-not-the-absolute-numbers">Savings rate is key, not the absolute numbers</h2>
<p>MMM explains that the absolute numbers (how much you earn, and how much you save) aren’t as as important as your <code class="highlighter-rouge">savings rate</code> which <code class="highlighter-rouge">= amount you save / amount you earn after tax</code>.</p>
<p>To illustrate why, here are the two extremes:</p>
<ul>
<li><strong>Save 0%, and spend 100% of your income</strong>, you’ll never save a penny, and you’ll have to bank on the state pension at 60something (or more likely 70something) when you eventually retire</li>
<li><strong>Save 100%, and spend 0% of your income</strong> (i.e. live for free) and you could stop working and retire now (assuming you can maintain this lack of spend if you stopped working)</li>
</ul>
<p>If your savings rate is somewhere in the middle, you’ll become financially independent somewhere in the middle too. Here’s a chart that shows a little more - <em>years to FI vs savings rate</em>.</p>
<h2 id="a-higher-savings-rate-accelerates-the-time-to-fi">A higher savings rate accelerates the time to FI</h2>
<p>This chart below shows that the time it takes to get financially independent <em>does not</em> scale linearly with your savings rate.</p>
<iframe width="746.3611859838275" height="461.5" seamless="" frameborder="0" scrolling="no" src="https://docs.google.com/spreadsheets/d/e/2PACX-1vRvEiL3wkLkXr_K55ur9ORXZepSQA8Fs0Dw2ZqwgDxwRbgj0UHyXDQ7AmoduBsILNpdPggXj9wFiW43/pubchart?oid=313112970&format=interactive"></iframe>
<p>The beauty of having a higher savings rate is that you’re not only <em>saving more money, faster</em> but you’re also <em>spending less</em>, and need less money overall to retire. These two things have a compounding effect, and can rapidly accelerate financial independence. That’s why the graph isn’t linear, it’s exponential.</p>
<h2 id="what-does-this-mean-for-you-in-practice">What does this mean for you, in practice?</h2>
<p>This grid, for UK audiences, is appropriated and adapted from <a href="https://fourpillarfreedom.com/the-early-retirement-grid/">this one</a> by US-based Four Pillar Freedom.</p>
<p>It tells you, for each post-tax income (the x-axis) and spend (y-axis) combination, how long it’ll take you to retire (in years).</p>
<p><img src="/assets/img/classical-fi/retirement-grid.png" alt="Net pay per hour" /></p>
<p>The assumptions I’ve used are:</p>
<ul>
<li>3.5% interest rate (above inflation) on savings</li>
<li>3.0% safe withdrawal rate (see end of article for references on why)</li>
<li>£0 initial savings</li>
</ul>
<p>If you already have some savings, ping me an email :email: and I can send you a spreadsheet that will let you factor this in.</p>
<h2 id="its-all-about-widening-the-gap">It’s all about widening the gap</h2>
<p>The key thing this chart should tell you is that the wider the gap between what you earn and what you spend, the quicker you can retire. Exponentially quicker in fact.</p>
<p>For example, <strong>if you’re in the £35k to £45k post-tax region, spending £15k a year vs £30k could mean you retire in 13 years rather than 35 years</strong>. That’s an enormous difference.</p>
<p>If you’re starting at 25, that’s retirement at 40, not 60 :open_mouth: . Those are some peak years.</p>
<p><br /></p>
<h3 id="read-on-for-some-maths">Read on for some maths…</h3>
<p><br /></p>
<h2 id="how-does-the-maths-work">How does the maths work?</h2>
<p>I’ve dug into this to understand more.</p>
<p>We want to work out how long will it take to become financially independent (FI) for different savings rates. Let’s call this time period “n”.</p>
<p>Financially independent means your expenses are covered by the safe amount you can withdraw from your “futureSavings”. So we’re going to write an equation that helps us to find ‘n’ when the futureSavings have grown big enough to support a withdrawal rate of 3% that covers your expenses.</p>
<h4 id="there-are-six-key-variables">There are six key variables</h4>
<div class="highlighter-rouge"><div class="highlight"><pre class="highlight"><code>startingPot: £X,000
interestRate: 3.5%
withdrawalRate: 3%
annualIncome: variable
savingsRate: variable
futureSavings: variable
</code></pre></div></div>
<h4 id="equation-1-your-future-expenses">Equation 1: your future expenses</h4>
<p><code class="highlighter-rouge">FIExpenses</code> = how much you’ll spend per year when you’re financially independent.</p>
<p><code class="highlighter-rouge">Withdrawal rate</code> = how much of your savings pot you’ll be <a href="https://www.investopedia.com/terms/s/safe-withdrawal-rate-swr-method.asp">safe to withdraw</a> per year</p>
<div class="highlighter-rouge"><div class="highlight"><pre class="highlight"><code>FIExpenses = withdrawalRate * futureSavings
</code></pre></div></div>
<p>We’ll assume you’ll spend the same in retirement as you will now. So FIExpenses = currentExpenses</p>
<div class="highlighter-rouge"><div class="highlight"><pre class="highlight"><code>currentExpenses = withdrawalRate * futureSavings
</code></pre></div></div>
<p>Our current expenses are <em>also</em> a function of our savings rate:</p>
<div class="highlighter-rouge"><div class="highlight"><pre class="highlight"><code>currentExpenses = (1 - savingsRate) * annualIncome
</code></pre></div></div>
<h4 id="equation-2-your-future-savings">Equation 2: your future savings</h4>
<p>After n years, your savings will be a combination of the pot of money you started with, and the money you saved along the way (a function of your savings rate). Both of these will be growing with a particular interest rate.</p>
<div class="highlighter-rouge"><div class="highlight"><pre class="highlight"><code>futureSavings after n years = [Starting pot after n years] + [Ongoing monthly payments after n years]
</code></pre></div></div>
<p>We can calculate how the starting pot will grow, using a compound interest calculation. We’ll call this <code class="highlighter-rouge">futureSavings A</code>.</p>
<p>The ongoing payments are a little tricker (a future value series, see the reference below. We’ll call this one <code class="highlighter-rouge">futureSavingsB</code>.</p>
<p>Here are those equations:</p>
<div class="highlighter-rouge"><div class="highlight"><pre class="highlight"><code>futureSavings = futureSavingsA + futureSavingsB
futureSavingsA = startingPot * (1+interestRate)^n
(this is just compound interest)
futureSavingsB = (annualIncome * savingsRate) * ((1+interestRate)^n - 1) / interestRate
(this is a future value series, see reference below)
</code></pre></div></div>
<h4 id="combine-the-two-equations-and-rearrange">Combine the two equations and rearrange</h4>
<p>We take this, combine it with the expenses formula earlier, and rearrange to remove <code class="highlighter-rouge">FutureValue</code> and <code class="highlighter-rouge">CurrentExpenses</code>.</p>
<div class="highlighter-rouge"><div class="highlight"><pre class="highlight"><code>Equation 1) currentExpenses = futureSavings * SWR%
Equation 2) currentExpenses / withdrawalRate = [startingPot * (1+interestRate)^n] + [(annualIncome * savingsRate) * ((1+interestRate)^n - 1) / interestRate]
Combined Equations) ((1 - savingsRate) * annualIncome)) / withdrawalRate = [startingPot * (1+interestRate)^n] + [(annualIncome * savingsRate) * ((1+interestRate)^n - 1) / interestRate]
</code></pre></div></div>
<p>We do some fairly heavy rearranging, and then take the natural logarithm of either side (see reference below).</p>
<h4 id="an-equation-to-find-n-years-to-fi-based-on-savings-rate">An equation to find ‘n’ (years to FI) based on savings rate</h4>
<div class="highlighter-rouge"><div class="highlight"><pre class="highlight"><code>n = (ln((annualIncome * (interestRate * (-savingsRate) + interestRate + savingsRate * withdrawalRate)) / (withdrawalRate * (annualIncome * savingsRate + initialValue * interestRate)))) / (ln(interestRate + 1))
^^NOTE: this uses logarithms
</code></pre></div></div>
<p>And that’s what you pop into Excel to generate the chart above :thumbsup: .</p>
<p>References:</p>
<ul>
<li><a href="https://retirementresearcher.com/4-rule-work-around-world/">Safe withdrawal rates for the UK</a></li>
<li><a href="http://financeformulas.net/Future_Value_of_Annuity.html">Future value of an annuity</a></li>
<li><a href="https://en.wikipedia.org/wiki/Natural_logarithm">Natural logarithm</a></li>
</ul>Hint: it's all about your savings rateHow much do you really earn?2019-03-30T11:26:18+00:002019-03-30T11:26:18+00:00https://onfi.co.uk/maths/careers/2019/03/30/how-much-really<p><code class="highlighter-rouge">Start thinking post-tax, per hour</code></p>
<h1 id="we-choose-careers-based-on-gross-pay-per-year">We choose careers based on gross pay per year</h1>
<p>Lots of people I know chose corporate jobs as they “pay well”. Starting salaries in the £40ks and £50ks lure people into consulting, banking and law without much thought.</p>
<p>I don’t think they’re looking at the right metric.</p>
<h1 id="we-should-choose-jobs-based-on-net-pay-per-hour">We should choose jobs based on net pay per hour</h1>
<p>A better metric should be <em>net</em> pay per hour.</p>
<p>Why? It reflects real (i.e. post tax, in your pocket) income, and brings time spent working into the equation.</p>
<p><img src="/assets/img/how-much-really/netpayperhour.png" alt="Net pay per hour" /></p>
<p>In most jobs we’re exchanging our time for money, so it makes sense to understand the price tag we’ve put on that time. Then we can properly assess whether we think that’s a fair exchange.</p>
<p>The <a href="https://www.livingwage.org.uk/calculation">London Living Wage</a> is £10.15 per hour. Assuming someone works a 40hr week, this will drop to about £8.53 post-tax. If you’re earning somewhere in the £40ks but working a 60 to 70 hour week, you’re probably just earning the living wage.</p>
<h1 id="graduate-lawyers-earn-less-than-a-civil-servant">Graduate lawyers earn less than a civil servant</h1>
<p>If you’re optimising for gross annual salary, hopefully you can see that your earnings aren’t <em>quite</em> as spectacular as you think. I assume most graduate bankers don’t expect to be earning the London Living Wage.</p>
<p>To put it in context further, we can compare the salaries for different career choices, at three stages: graduate level, three years in and five years into your career (I’ve made a few assumptions, based on anecdotal data from friends here).</p>
<p><img src="/assets/img/how-much-really/netpaybycareer.png" alt="Net pay per hour" /></p>
<p>This tells us a few things:</p>
<ul>
<li>Bankers and civil servants consistently earn <em>roughly</em> the same per hour</li>
<li>Graduate law and banking jobs will milk you, with the lowest pay per hour</li>
<li>As you get more experienced, law pay does start to get ahead of civil service</li>
<li>Software engineers are, on balance, killing it</li>
</ul>
<h1 id="life-isnt-just-about-money-its-about-freedom-too">Life isn’t just about money, it’s about freedom too</h1>
<p>This post is intentionally provocative. Obviously going into banking and law will mean you end up with more money - at an aggregate level - but is it worth it?</p>
<p>In the most time-consuming jobs - like banking and law - you can end up working over 60 days extra per year on your public sector or software engineering pals. That’s 60 full, 24 hour, days extra per year.</p>
<p>If you assume a ‘normal’ working day is 8 days, those 60 extra days actually become 180 extra working days. I.e. half a year’s worth of extra working, every year.</p>
<p>:no_mouth:</p>
<p>That’s a lot of time you take away from other things. Like seeing friends for a drink or dinner or the theatre mid-week. Like talking to your family, or partner. Like exercising, and staying in good shape. Like making the most of sunny summer evenings in <a href="https://assets.londonist.com/uploads/2017/07/i875/p18__victoria_park_pavilion_and_cafe_by_the_lake_in_london_borough_of_tower_hamlets_-copyright_peter_jeffree.jpg">Victoria Park</a> or <a href="https://media.timeout.com/images/103163980/750/562/image.jpg">London Fields</a>.</p>
<p>Yes, you may say “I’ll do banking for a bit, get loaded and then stop”, but it rarely plays out like that. See <a href="https://ecorner.stanford.edu/video/a-cautionary-word-on-the-deferred-life-plan/">here</a> and <a href="https://lettersfromtheporch.wordpress.com/2009/09/26/on-the-deferred-life-plan-an-introduction-to-randy-komisar/">here</a> for more thoughts on the “deferred life plan”, and why it’s a bad choice.</p>
<p>Most people don’t <em>really</em> want to retire in their 30s, they want to enjoy their job and have time to spend doing things they enjoy. We tend to place too much emphasis on the total number, and discount the extra time needed to generate it.</p>
<p>This is particularly worth bearing in mind if you’re starting out in your career. Do you really want to be missing out on your twenties?</p>
<h1 id="commute-flexibility-and-other-things-to-think-about">Commute, flexibility, and other things to think about</h1>
<p>When you’re doing these calculations and thinking about careers, it might be worth thinking about a few other variables:</p>
<ul>
<li>Commute time</li>
<li>Flexible working</li>
<li>Part-time working</li>
</ul>
<p>First, <strong>commute time</strong>. When we consider commute time the picture can change substantially. I currently cycle 20mins to work, but I know some people who commute over an hour each way. That’s an extra 6.5hrs per week that they lose for work. That will definitely bring the pay per hour down.</p>
<p>Second, <strong>flexible working</strong>. The commute becomes irrelevant if you can work from home regularly. Lots of companies are starting to encourage this, and all the associate life/health/happiness benefits it brings. Not only that, but in the wider context of financial independence you can dramatically cut your living costs whilst maintaining your salary.</p>
<p>Finally, <strong>part-time working</strong>. Software engineers earn a great rate per hour. There’s no reason someone on a £80k+ salary couldn’t just drop down to 4 days a week. Worth bearing in mind?</p>Start thinking post-tax, per hour