Saturday, April 5, 2014

'E' is for ... well, ... e

'E' is for ... wait for it: ... e.

The number e is this neat little number that shows us that mathematics isn't for just us pencil-necked geeks with our pocket protectors.

Okay. Seriously. Did they have to go there in WarGames with the whole "Mr. Potato-Head! Mr. Potato-head!" Seriously? We, the geeks of the world, are not all like that.



Anyway, I digress.

(Do you think I love digressing? No, not at all, it's just who I am and what I do. That's how I'm rollin' wid it, baybee!)

Okay, so, fer realz, yo: the number e. You can't point to it on a number line ...

Unless you go:

| --- | ---- | ---- |
0    1      2    e3

And there's your e ... kinda, sorta, I just pointed to it.

But 'e' is eminently useful, as it shows up in calculus, particularly for the 'natural' logarithm.

But why? Why do we want to scale along the number e?


Did I get your attention?

Bernoulli came along one day when someone asked him, 'Hey, I know I get money back when I put money into a bank that pays interest annually, but how much, if any, more will I get back if they compound more often?"

Money, compounded continuously falls along the exponent of the number, so, to compute your mortgage or your interest in your savings, you use the 'Pert' formula.

And, yes, you look lovely! in that dress, you Pert thing!

'Pert' is this:

P = principal (what you put in)
e = e (duh!)
rt is 'rate times time (in years)'

So, really it's:


Or, written on your calculator or on your computer in a spreadsheet:

P * exp(r * t)

So, if you put in $1,000 for a year in a bank paying 5.25% interest

(Don't laugh, that's what I did when I was a wee one, wet behind the ears. Remember when savings account used to payout at that rate? No, you don't, because you weren't born then)

(But I digress)

Then you simply use your Pert formula and come to find that you have:


If the bank had paid interest only once per year, you would've only had

$1052.50 (of course).

A buck-fifty. Big whoop.

The big whoop is this. Do that for 20 years, 30 years, 40 years ...

You'll start to see a huge difference between compounding simply and compounding continuously.

That's your savings. The banks are doing the same thing with you.

You have credit cards? You have a mortgage?

A general I knew used to say, nearly every day: "30-year mortgages are killing our nation's finances!"

Pay off your debts. The longer you take to pay, the more that little number e is going to crush you under its accumulated weight.

And the reverse is true, the bit extra you pay now against the principal you owe? It translates into a factor of five or ten or twenty-fold, depending on the interest rate and the time of the loan.

Knowing a little bit of math can actually help you decide things more prudently for the long term.

1 comment:

Nicki Elson said...

Hey! This is something I actually sort of know from my finance major days. :)

Sorry I've been missing - just got back from the World that is Disney so I'm easing into this A to Z thang.