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Comment by GeoAtreides | Hacker News Reader

> As a mathematician, I had trouble understanding how banks calculate it (as they would obviously not point me at the derivation of the formula)

This is not true? The formula is well known:

A = P*e^(rt)

where"

A = Final amount

P = Principal (initial investment/loan)

r = Annual interest rate (as a decimal)

t = Time in years

e = Euler's number

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A loan is subdivided and sold in different allotments each year at a different interests rate, principal, and terms. You want to sell the entire debt at some point in the future. How do you calculate the price such that you don’t sell at a loss?

Why does that formula work? ;)

I did not say "derivation of the formula" by accident: this is about why would this produce something that makes sense as "interest-as-percentage"?

That is the integral

You're assuming banks use that formula and not just YOLO it, "haha fuck you pay me more".

If you learnt calculus, you could check their work and see that it's accurate. And it only takes algebra and a few minutes of work to see that your bank statements match the formula that's been given.

I know calculus, and I also know that mortgage payments don't follow that formula - or, maybe they do but they're so buried in noise and extra charges and costs you'd never know it.

Bookkeeping normally computes interest based on some accounting period - days, weeks, months, or quarters. It's a sum of discrete charges, not an integral. It was usually monthly in the paper and pencil era; today it is usually daily. Look up "double declining balance" and "Rule of 73".

Financial calculators do integrate, though. "Present value" is computed by integration.

Generally, banks try to get as much of the interest early on, and move the base to later. This is why it usually makes no sense to pay off a debt after 5 or 10 years when you paid 80% of the interest already (but also why refinancing works for banks: more upfront interest which they put into books as profit right away).

On some things, governments put the cap on how much can early payments be loaded with interest and how much at least should be paying off the base debt — otherwise, you'd be paying only the interest for the first 15 years of a mortgage.

Though, these things work slightly differently in different countries.

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