There are num­bers that look small and be­have large. If you want to be good with mon­ey and to be on top of your per­son­al fi­nances you should take the time to un­der­stand this re­al­i­ty.

I am cer­tain if I were to head­line this col­umn as “log­a­rith­mic think­ing mat­ters” many of you would switch off or start read­ing with a men­tal block. In plain lan­guage, all I am say­ing is that you should as a mat­ter of course be ask­ing not on­ly, “How much big­ger is this?” but, “How many times big­ger is this?”

What we are dis­cussing here is a way of read­ing scale cor­rect­ly, and this is ex­treme­ly im­por­tant to your un­der­stand­ing of your fi­nan­cial world.

Earth­quakes of­fer a good way to il­lus­trate the con­cept out­side of fi­nance. The mea­sure­ment of an earth­quake mag­ni­tude is log­a­rith­mic. Ac­cord­ing to the US Ge­o­log­i­cal Sur­vey, each whole num­ber in­crease in mag­ni­tude means ten times greater mea­sured wave am­pli­tude and about 32 times more en­er­gy re­leased.

On June 24, 2026, two large 7.1 and then 7.5 earth­quakes struck north­ern Venezuela with­in less than a minute. Al­most 2,000 are now dead and many times more are miss­ing, in­jured and dis­placed.

The ini­tial read was a 7.2 and a 7.5. You might think that 7.2 and 7.5 are close enough not to mat­ter much. The dif­fer­ence is on­ly 0.3 on pa­per, but on a log­a­rith­mic earth­quake scale it means the larg­er quake re­leased about 2.8 times as much en­er­gy. The dec­i­mal point makes the dif­fer­ence look in­con­se­quen­tial but as you can clear­ly see, there are huge life chang­ing dif­fer­ences to these small num­bers.

Read­ing about the earth­quake, shows how bad­ly our in­stincts can fail when a num­ber is writ­ten on a scale we do not un­der­stand and this same mis­take oc­curs every day in per­son­al fi­nance.

When it comes to our mon­ey all of us want growth. We want eco­nom­ic growth, we want our in­comes to grow, we want our in­vest­ments to grow. When we think about growth we think about com­pound­ing. We want to earn $100. Then earn 5 per cent on that $100 so that it be­comes $105 af­ter one year and $110.25 af­ter two years. The sec­ond year earns a re­turn on both the orig­i­nal $100 and the first year’s $5.

Scales

Most of us aim for com­pound­ing and then stop, we don’t take the time to un­der­stand the log­a­rith­mic scales at­tached to our mon­ey. For starters, a log­a­rith­mic scale is not a growth process. It is a mea­sur­ing tool. It helps us un­der­stand things that grow or shrink by mul­ti­pli­ca­tion. It turns re­peat­ed mul­ti­pli­ca­tion in­to even steps. If you think of com­pound­ing as the en­gine, log­a­rith­mic think­ing is your dash­board. If you are dri­ving your car and the in­stru­ment pan­el isn’t work­ing you will even­tu­al­ly run in­to prob­lems.

Take a sim­ple ex­am­ple. If mon­ey grows from $10,000 to $20,000, it has dou­bled. If it grows from $100,000 to $200,000, it has al­so dou­bled. The sec­ond in­crease is $100,000 and the first is on­ly $10,000, but as in­vest­ment per­for­mance they are the same: each is a 100 per cent gain. A log­a­rith­mic chart treats those two dou­blings as equal moves be­cause it is read­ing per­cent­age change, not dol­lar change.

This is why long term in­vest­ment charts are of­ten clear­er on a log scale. A nor­mal chart gives equal vi­su­al space to equal dol­lar moves. A log chart gives equal vi­su­al space to equal per­cent­age moves. For a long term in­vestor, per­cent­ages and mul­ti­ples mat­ter be­cause wealth com­pounds by per­cent­age re­turns.

Log­a­rith­mic think­ing al­so helps us un­der­stand time. Sup­pose you in­vest $10,000 and hope to reach $40,000. In your mind you need an­oth­er $30,000. To be able to achieve it, you need a process and here your log­a­rith­mic mind says you need to mul­ti­ply your mon­ey by four, which means two dou­blings. At 7 per cent a year, mon­ey rough­ly dou­bles every decade. So, with­out adding more con­tri­bu­tions and ig­nor­ing tax­es and fees, two dou­blings take a lit­tle over 20 years.

If you ap­ply this think­ing to fees then you will be­come more ju­di­cious about how much you pay for a re­cur­ring ser­vice. A 1 per cent an­nu­al fee to man­age your in­vest­ment sounds small. But it is not paid once. It comes out every year, re­duc­ing the amount left to com­pound. For ex­am­ple $100,000 grow­ing at 4 per cent an­nu­al­ly for 20 years: with a 0.25 per cent fee, the port­fo­lio ends around $208,000; with a 0.50 per cent fee, around $198,000; with a 1.00 per cent fee, around $179,000. The small an­nu­al dif­fer­ence be­comes a large fi­nal dif­fer­ence be­cause it re­peats.

This does not mean the cheap­est prod­uct is al­ways the best prod­uct. Ad­vice, tax plan­ning, dis­ci­pline and ac­cess can have val­ue. But re­cur­ring costs must earn their keep. A fee is not just a line item. It is a claim on fu­ture com­pound­ing.

Ru­in

Loss­es are an­oth­er place where every­day think­ing mis­leads. If a port­fo­lio falls 50 per cent, it will not re­cov­er with a 50 per cent gain. It needs a 100 per cent gain. Start with $100. Lose half and you have $50. To get back to $100, the re­main­ing $50 must dou­ble. This is ob­vi­ous once shown, but in­vestors for­get it, of­ten time lead­ing to com­pla­cen­cy in how they man­age their in­vest­ments.

That is why avoid­ing ru­in mat­ters more than chas­ing every pos­si­ble gain but yet peo­ple’s over­whelm­ing em­pha­sis is on how much mon­ey can be made as op­posed to the risk as­so­ci­at­ed with earn­ing that re­turn.

Volatil­i­ty al­so re­duces what in­vestors ac­tu­al­ly earn. Imag­ine an in­vest­ment ris­es 30 per cent one year and falls 20 per cent the next. The av­er­age of plus 30 and mi­nus 20 is plus five. But $100 be­comes $130, then $104. The end­ing wealth is on­ly 4 per cent high­er af­ter two years. The arith­metic av­er­age looked bet­ter than the lived re­sult.

This is why the path mat­ters. Per­son­al fi­nance is not a spread­sheet of av­er­age re­turns. It is a se­quence of de­ci­sions made un­der un­cer­tain­ty: whether to hold cash, bor­row, di­ver­si­fy, sell in a pan­ic, pay high fees, or in­vest mon­ey that may be need­ed next year. The or­der of events can mat­ter as much as the av­er­age.

Log­a­rith­mic think­ing al­so ex­plains why di­ver­si­fi­ca­tion is so im­por­tant. Di­ver­si­fi­ca­tion can­not guar­an­tee that in­vest­ments will not suf­fer in a mar­ket drop, but it can im­prove the chances that loss­es are small­er than they would be with­out di­ver­si­fi­ca­tion. This is im­por­tant be­cause a deep loss is not just emo­tion­al­ly painful. As I have showed above, it math­e­mat­i­cal­ly rais­es the hur­dle for re­cov­ery.

The same ap­proach al­lows you to see the val­ue in start­ing to save be­cause start­ing has a dis­pro­por­nate im­pact. Think about the sum of $10,000. If your start­ing point is $1 then at the end you have $10,000. If your start­ing point is $1 mil­lion then at the end you have $1.01 mil­lion. It’s the same $10,000 in each case but for the per­son start­ing at $1 that end­ing amount is much more con­se­quen­tial.

This is an­oth­er ex­am­ple of the log­a­rith­mic feel: the first lay­ers of se­cu­ri­ty mat­ter most. Af­ter that, mon­ey still mat­ters, but each ad­di­tion­al dol­lar may add less im­me­di­ate safe­ty.

This is why sen­si­ble fi­nan­cial plan­ning be­gins with re­silience. Pay down de­struc­tive debt. Build a cash buffer. In­sure against risks that could wreck the house­hold. Keep mon­ey need­ed soon away from volatile as­sets. Then in­vest long term mon­ey pa­tient­ly and at rea­son­able cost. This is the ar­chi­tec­ture that lets com­pound­ing work, ex­cept that most just want the com­pound­ing and fail to set up the ar­chi­tec­ture.

Log­a­rith­mic think­ing does not pre­dict the next earth­quake or the next mar­ket crash. It does some­thing more use­ful. It teach­es us to re­spect scale. It teach­es us that a small num­ber on the scale may hide a large force. It teach­es us that a small an­nu­al per­cent­age, re­peat­ed for decades, can change a life. It teach­es us that loss­es, fees and debt are dan­ger­ous not on­ly be­cause they hurt to­day, but be­cause they re­duce to­mor­row’s base.

The record of the Venezuela earth­quakes re­minds us that num­bers must be read in their own lan­guage. Per­son­al fi­nance asks the same dis­ci­pline of us. Read re­turns as mul­ti­pli­ers. Read fees as re­cur­ring drags. Read loss­es as dam­age to the base. Read time as the friend of the pa­tient and the en­e­my of the over­lever­aged. Read charts in per­cent­ages, not just dol­lars.

Just as we have on seis­mol­o­gist to in­ter­pret earth­quake num­bers, your fi­nan­cial pro­fes­sion­al should help you un­der­stand your fi­nan­cial num­bers.

Ian Nar­ine is a fi­nan­cial con­sul­tant who logs his columns to scale. Please send your com­ments to

ian@ian­nar­ine.com