| ▲ | necovek a day ago |
| > Whether the infinite-series summation limits are worth knowing is questionable, though. That's more of historical interest. A very common example is compound, continual interest accumulation. As a mathematician, I had trouble understanding how banks calculate it (as they would obviously not point me at the derivation of the formula), but it's actually a limit sum over infinitely small interest terms. Similarly, these techniques work to explain and derive numerical methods for calculating many natural constants like e, pi etc. |
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| ▲ | 1-more a day ago | parent | next [-] |
| The only intuitive definition of e I can remember is "how much $1 becomes after a year in a savings account with 100% interest compounded infinitely" funny enough. |
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| ▲ | GeoAtreides 20 hours ago | parent | prev | next [-] |
| > 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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| ▲ | fingerlocks 20 hours ago | parent | next [-] | | 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? | |
| ▲ | necovek 19 hours ago | parent | prev | next [-] | | 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"? | |
| ▲ | fooker 18 hours ago | parent | prev | next [-] | | That is the integral | |
| ▲ | ErroneousBosh 19 hours ago | parent | prev [-] | | You're assuming banks use that formula and not just YOLO it, "haha fuck you pay me more". | | |
| ▲ | fwip 14 hours ago | parent [-] | | 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. | | |
| ▲ | ErroneousBosh 13 hours ago | parent [-] | | 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. | | |
| ▲ | Animats 7 hours ago | parent [-] | | 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. |
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| ▲ | parkcedar a day ago | parent | prev [-] |
| Where I live, the banks say that they compound interest daily, but pay interest monthly. So, I think the small interest term is just limited to a day where the error is small enough for the average person to not care. |
