I'm teaching exponential relationships to my class tomorrow morning and one of the applications of this understanding is obviously debt.

We just got finished discussing linear relationships last week, and it got me thinking: why is the accumulation of interest not linear? You've only borrowed the principal, so in my mind, if you're going to have interest, it would be proportional to the amount of the principal you haven't paid off yet.

Thinking like a lib (or maybe not since I can't understand the way it actually works), the lender would be unable to access a certain amount of money that they previously did have access to, and thus would be privy to a proportion of that amount. As you pay on the principal, that amount should go down because they have more access to the money they previously had access to.

What purpose does your interest creating more interest serve other than simply to siphon money from the ones that need to borrow and those that have enough to lend?

Obviously that is the reason, but I'm just curious if there's an actual reason they have, or if they really are just that blatant.