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.
I think it will help to see money as a relation, rather than a static thing. Then I’ll give some examples. I’m no expert but I think working through some examples will be helpful.
If I had $1000 in my bank today, I could buy $1000 worth of stuff today. In a year’s time, I could maybe buy $900 worth of stuff, because prices are going up. Meaning, $1000 might still be called $1000 and look like the same $1000. If it were under my mattress, it may even be the same 20x$50 notes. But it isn’t the same $1000; what I can use it for depends on a wide range of factors, including inflation. The number in the account may be static, but the number only means something as a relation.
If I lend you that $1000 at 3% for one year, you pay me $1000 plus $30. By the time you pay me, prices have gone up. You’ve only really paid me back $900+$30 worth of stuff (‘ish’, because the $30 isn’t worth as much, either).
I could charge simple interest at the rate of inflation and break even, more-or-less. But what if you take two years to pay? Do I charge compound interest at 10%/year or (if my maths are correct) simple interest at 21%/biennially? Do I adjust the simple figure if you pay me back early?
Compound interest seems to be a more straightforward way of working out how much the borrower needs to repay to actually repay what was borrowed (relationally, i.e. what the money can buy) rather than the initial sum (e.g. the static $1000). You only actually pay interest on interest if you borrow too much and can’t pay off more than the yearly addition. People don’t always have a choice, of course, house prices being what they are, for example.
When you borrow money from a bank as a loan, you get both figures. Or an approximation (because interest rates fluctuate and debtors can make overpayments). Consider a mortgage. You get e.g. the ‘5.7%/year (compound)’ and you get a typical estimate of the overall interest, e.g. $75,000 on a mortgage of $100,000 if you take 35 years to repay.
Not everyone who borrows that money will actually repay the $75,000. You could borrow the $100,000 at 75% but then you risk losing out if the base rate or inflation go down or if you get a pay rise that would let you make overpayments.
Compound interest can work in the borrower’s favour as well as the lender’s. It’s perhaps easier to see with commercial loans, where the borrower and lender have more equal bargaining power. Maybe the borrower has more bargaining power. Compound interest is not always ‘unfair’ in a straightforward way.
Compound interest is monstruous, don’t get me wrong, and compound interest is a factor in prices going up, but it has a certain logic to it. As for the bourgeois rationale, it’s going to be something like the above but without the words ‘relational’ and ‘static’.