# Additive vs

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If you think way back to grade schoolgebouw, you may reminisce that you studied addition and subtraction one year, and then a grade or two zometeen studied multiplication and division. Each pair of arithmetic operators intrinsically go together – they’re opposites of each other (algebraists would say inverses). What I want to explore today is that each pair of arithmetic operators carries with it a means of thinking about numbers, and thus by extension thinking about money. Thesis two means of thinking are both useful but they’re remarkably distinct, and people frequently make the mistake of applying the wrong type of thinking te a given circumstance. My entire premise here may seem irredeemably nerdy, and it is. But bear with mij anyways – I reckon there’s vivo insight to be had.

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Additive thinking about money is everywhere. It’s associated with he arithmetic operators addition, subtraction, and subtraction’s close relative comparison. Every bit of frugality advice clogging the internet is additive te nature – when you skip buying that $Four cup of coffee, you’ve added (or declined to subtract) $Four from your wallet. Our putative frugalist might remind you that overheen time thesis little decisions add up. Which of course is true. But you could twist that idea around and say the only thing those skipped cups of coffee can do is add up. I’ll bet you’ve never heard anyone say that… wij’ll revisit it momentarily.

Additive money crops up ter other places – when people discuss their incomes, or compare them, they’re indeed looking at the amount of money they added to their stash this year. The same could be said for discussions of paying off your mortgage – how much did you subtract from the loan principle? Saving, spending, earning, paying off – it’s all additive. You might say the financial blogsphere is badly additive te treatment.

One of the interesting features of additive finances is that events are independent. If you spend $Four on a latte today and $Two on a pack of gum tomorrow, you’re down $6. The two decisions have no influence on each other – if you didn’t buy the latte, the gum would still cost $Two. For a lotsbestemming of financial situations, this sort of independence is exactly the case so thinking about them ter an additive way is very effective.

Of course there are lots of financial matters that don’t have this property. For starters, there’s anything with an rente rate. If you waterput X dollars te an rente bearing account at 2% plain annual rente, after the very first year you’ll have (1.02 * X) dollars. But after the 2nd year, you’ll have (1.0404 * X) dollars. The two years are not independent – at the commence of year Two you have more money ter your account than you did at the embark of year 1 because of what happened te year 1 – the events are linked. This idea is frequently trained spil the “magic” of compounding rente, which when you get right down it isn’t necessarily all that magical spil XKCD reminds us. But this is unquestionably a different zuigeling of thinking about money – te order to calculate how much money you’d have at the end of year Two, I had to multiply 1.02 * 1.02. Wij’ve left the field of additive money and entered the field of multiplicative money.

You can find multiplicative money te places much more intriguing than rente rates – think about job hopping and salary. If I hop from job A to job B and negotiate a 20% raise, and then three years zometeen do it again, I’m now making 1.44x what I wasgoed before (disregarding other possible raises). Salary negotiations are multiplicative, and spil a result of some good career moves I made early on I’m going to make much more, most likely for life. Te tegenstelling, getting laid off and subsequent unemployment is like multiplying by a número less than one – if you have to take a job that pays 75% spil much spil you used to make to get back to being employed, that likewise could lightly go after you for life – multiplied into each future salary negotiation.

I mentioned before that people frequently apply the wrong type of thinking. This can go both directions, but ter the salary case it’s effortless to fall into additive thinking when you should be thinking multiplicative. Consider this half-assed attempt at instructing people how to negotiate salary. I’ve got news for you – worrying about the job’s expense account isn’t going to matter much. Worrying about your hair dye job is just vapid. What’s going to matter when it comes down to hardball negotiation is your walk-away number, and that’s a function of your old salary multiplied by the ondergrens benefit you’re willing to realize due to the job hop. You should be thinking multiplicative, and those tips are at best additive.

Now, spil the XKCD comic above reminds us, repeated multiplication doesn’t always produce dramatic results. Getting big things to toebijten is dependent on four inputs:

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- Where you begin
- What the multiplication creador is
- How many times you multiply
- What inflation is

This explains why the XKCD result is so banal – the commencing point is low ($1000), the multiplication creador is lil’ (1.02) and the number of multiplications is pretty low (Ten). Nothing titillating is going to toebijten. When you creador ter inflation overheen Ten years (inflation is presently about 2%) the results are going to be so close to pauze even spil to be irrelevant.

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Now tegenstelling that with the salary negotiations. The embarking point is much higher (10s of thousands of dollars vanaf year of salary) and the multiplication factótum is much fatter (1.Two). So instead it takes about Four 3-year periods to dual your salary – 12 years vs. XKCD’s Ten. It would take about 15 year to dual the salary if you factótum te today’s inflation. But at the end the results are indeed something worth talking about. Life switching even.

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It’s also possible to make mistakes the opposite direction. I see people do this all the time when dealing with savings accounts. They go out of their way to sign up for an account with a comparatively high rate (Ally is suggesting 0.84% right now vs. 0.10% at my credit union) and waterput say $2000 ter the account. Guess what – this brilliant stir is going to make you a whopping $17 vanaf year. If you waste even one hour dicking around getting the account set up, there goes your profit for the next few years. Multiplicative thinking is downright impotent here – you’d make a thicker dent ter your finances by not buying lattes. Wij can start to see the normal rule: puny money and puny rates confianza additive thinking. Big money and/or big rates honra multiplicative thinking.

This means multiplicative thinking matters under two conditions:

- when you’re so deep te debt the rate you’re paying on your debt determines your financial outcome
- when you’re so wealthy the come back on hacienda you’re getting on your wealth determines your financial outcome.

Ter the middle zone inbetween those two, additive thinking rules. Incidentally, this goes a long ways towards explaining why the rich seem “out of touch” with middle class concerns. It’s because those concerns are additive and thus no longer meaningfully affect their outcomes. The latest faux outrage overheen Romney’s speaking fees is a prime example – he stated about $300K of speaking fees wasgoed “not very much”. This seems belachelijk from an additive perspective. Most people’s finances would be radically altered by a one-time $300K jolt. But it’s a plain statement of fact given Romney’s financial position – with something like $50M of working renta at his disposition (the precies number is private) those speakers fees represent less than a 1% switch te his situation. They’re even less relevant than XKCD’s 2% rente. It’s not very much. Similarly, Romney could never switch his financial situation via altering his coffee buying habits. Whether he buys no coffee whatsoever or all the overpriced lattes his bladder can hold, it won’t matter at all. All those lattes can do is add up – they can’t multiply.

Spil you might guess, the high finance world is much more interested ter multiplicative thinking than with additive. This makes flawless sense given the ample quantities of haber involved. Trading results are also inherently multiplicative – money made trading today can be used to take thicker positions tomorrow. This explains why being active ter the markets with limited hacienda is a fools errand, or training at best. Your trading results on $2000 of haber aren’t going to mean anything. They may help you learn to trade, but at that level of hacienda they will be predominated by additive effects elsewhere te your life.

Attempt this proef: whenever you encounter financial advice, ask yourself if it’s additive or multiplicative. And ask whether the problem supposedly being solved is best solved with that type of thinking.

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