## Monday, December 29, 2008

### Interest

(Click on the cartoon to see the entire image.)
(C)Copyright 2008, C. Burke. All rights reserved.

And I thought we could transcend all our differences...

It's been a while since I've been really, really mathy in one of these strips, so allow me to explain the Continuous compounding interest problem.

Basically, if you saved \$1 at an interest rate of 100% (great rate, isn't it?! That's why so much of math is theoretical although it has alleged practical applications -- but I digress), after one year that \$1 becomes \$2.

However, if that interest was compounded ever six months, after one year you would have \$2.25 instead.
Every four months would yield \$2.37.
Every three months would yield \$2.44.
Every two months would yield \$2.52.
Every month would yield \$2.61.
Every week would yield \$2.69.

And so on. As you see, the more often the interest is compounded, the more you get.
It is conceivable that a bank could compound your interest every hour or every minute! (There's that "theoretical" stuff again -- find me a real bank that does that, and I'll show you a bank that's looking for a big bailout. Okay, finding those is really easy on my end.)

It would seem that your \$1.00 could grow into millions given enough compounding, but in fact, it'll never yield more than \$2.72, and not because of greedy corporations, but because the smaller and smaller decimals you are dealing with will converge on a number beginning with 2.71828 18284 59045 23536.

A guy named Euler gave this number the imaginative name "e", not to be confused with the most frequently occurring letter in the English language, which just happed to be the first letter of his last name.