4 ms·

Here's what I don't understand about this: you won't do the long division in your head, so clearly, you'll have to memorise, for common interest rates, that 72/

by kqr 5y ago

Here's what I don't understand about this: you won't do the long division in your head, so clearly, you'll have to memorise, for common interest rates, that 72/2 = 36, 72/3 = 24, 72/4 = 19, 72/5 = 15, and so on. At that point, why wouldn't you just remember that "at 2 %, compounding doubles in 36 periods" and so on? Why the indirection through 72? (Obviously, if you need a more accurate calculation or you don't remember the division, you'll probably use an electronic calculator, and then you might as well compute the compounding directly. The only exception I can think of is if you don't have access to an electronic calculator but do have a slide rule at hand. This is very rare these days.)

dskloet 5y ago
72 = 2*2*2*3*3 so if the divisor is a multiple of those factors, the result is too. This makes the division quite easy in many cases. It's also why I immediately realized your typo in 72/4=19.
- iratewizard 5y ago
  Another way to say it is 3*4*6. Divide by those numbers by taking one of them out of the multiplication
Veserv 5y ago
Many people do actually do the division in their head, I certainly do and not just for the trivial divisors either. In fact, I would find it odd if any of my mathematically, scientifically, or financially inclined friends did not do it in their heads, at least for quick calculations, to the point where I actually find your position that people would just memorize it instead of calculating it kind of shocking. It is truly amazing how people can have such different life experiences.
- kqr 5y ago
  No, I get it. It might just be that mental division is a weakness of mine that I should brush up on.
  - nosianu 5y ago
    I usually do it by approximation most of the time. I estimate and then I multiply to see how close I got. Multiplication is easier. 720 / 13 for this example and 1.3% looks pretty easy this way IMO, you just need a few iterations. I immediately know the result of using 10, so I'm already down to 720/130, or 72/13. Which shows me I did something stupid because I could have started that way and not forgotten what "%" means in the first place... Anyway, using 5 as a very lazy first estimate gives me 5 * 13=65 - certainly manageable in most heads. Trying 6 gives me 78. Looking at both results, which have about the same distance from the target value, next I'll try 5.5 and that's 5 * 13 + a half of 13, still easy, 71.5. Close enough. Multiply by ten to compensate for the initial simplification, I get 55. That's really close to the result (~53.7, using the rule of 72 it is ~55.4). I try to segment such calculations into simpler ones, instead of doing one algorithm, and finding shortcuts. For the 5.5 I use the shortcut that it's half of ten which always is easy, and that I can split it into two easy parts. To me it's more fun that way, even if I could also do the algorithm. It's supposed to be fun and being lazy is my goal. For division you can often find shortcuts as well. Dividing by two, and powers of two subsequently, is simple enough. Any number you can divide by makes the number you have left easier. If you start from two you get prime factorization. You just have to remember a few numbers to put them together again (i.e. multiply) afterwards. Or any number less than ten really. Here too I would try to decompose. To me merely applying the algorithm is just work and maybe counts as mental exercise, but the decomposition and finding of little shortcuts is more fun and an exercise too.
  - quickthrower2 5y ago
    In terms of the 72 issue I guess it turns a general purpose skill (division) into a specific one (investment calculation). So to do it you brush up on division and unlock other skills, like I guess angles 360/6 and so on (which comes in useful at times)
  - kmill 5y ago
    Here's my one weird trick: work toward a PhD in mathematics, then get a postdoc, where you finally get assigned to teach courses like upper division undergraduate number theory. Thanks to this experience, I can tell you immediately what the factors of numbers like 6 and 15 are. 72 still takes some thinking, though.
stingraycharles 5y ago
> you won't do the long division in your head, so clearly, you'll have to memorise I think this assumption is false; at least for me, doing these types of divisions in my head is doable, I think we actually had to be able to do these types of calculations mentally in elementary school. Eg in your examples you say 72/2 = 36, so then 72/4 must be 18. I think the number 72 was chosen specifically for this property, that it divides easily for common values of interest rate (1, 2, 3, 4, 6, 8, 9 all divide cleanly).
reedf1 5y ago
It's already an approximation - you do not need to get precise with your division. Also - you should be able to do 72 divided by at least 2,3,4 (and estimate it for others), even by times tables/estimation and not long division.
deleted 5y ago
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by kqr 5y ago

dskloet 5y ago

72 = 2*2*2*3*3 so if the divisor is a multiple of those factors, the result is too. This makes the division quite easy in many cases. It's also why I immediately realized your typo in 72/4=19.

iratewizard 5y ago
Another way to say it is 3*4*6. Divide by those numbers by taking one of them out of the multiplication

Veserv 5y ago

Many people do actually do the division in their head, I certainly do and not just for the trivial divisors either. In fact, I would find it odd if any of my mathematically, scientifically, or financially inclined friends did not do it in their heads, at least for quick calculations, to the point where I actually find your position that people would just memorize it instead of calculating it kind of shocking. It is truly amazing how people can have such different life experiences.

kqr 5y ago
No, I get it. It might just be that mental division is a weakness of mine that I should brush up on.
- nosianu 5y ago
  I usually do it by approximation most of the time. I estimate and then I multiply to see how close I got. Multiplication is easier. 720 / 13 for this example and 1.3% looks pretty easy this way IMO, you just need a few iterations. I immediately know the result of using 10, so I'm already down to 720/130, or 72/13. Which shows me I did something stupid because I could have started that way and not forgotten what "%" means in the first place... Anyway, using 5 as a very lazy first estimate gives me 5 * 13=65 - certainly manageable in most heads. Trying 6 gives me 78. Looking at both results, which have about the same distance from the target value, next I'll try 5.5 and that's 5 * 13 + a half of 13, still easy, 71.5. Close enough. Multiply by ten to compensate for the initial simplification, I get 55. That's really close to the result (~53.7, using the rule of 72 it is ~55.4). I try to segment such calculations into simpler ones, instead of doing one algorithm, and finding shortcuts. For the 5.5 I use the shortcut that it's half of ten which always is easy, and that I can split it into two easy parts. To me it's more fun that way, even if I could also do the algorithm. It's supposed to be fun and being lazy is my goal. For division you can often find shortcuts as well. Dividing by two, and powers of two subsequently, is simple enough. Any number you can divide by makes the number you have left easier. If you start from two you get prime factorization. You just have to remember a few numbers to put them together again (i.e. multiply) afterwards. Or any number less than ten really. Here too I would try to decompose. To me merely applying the algorithm is just work and maybe counts as mental exercise, but the decomposition and finding of little shortcuts is more fun and an exercise too.
- quickthrower2 5y ago
  In terms of the 72 issue I guess it turns a general purpose skill (division) into a specific one (investment calculation). So to do it you brush up on division and unlock other skills, like I guess angles 360/6 and so on (which comes in useful at times)
- kmill 5y ago
  Here's my one weird trick: work toward a PhD in mathematics, then get a postdoc, where you finally get assigned to teach courses like upper division undergraduate number theory. Thanks to this experience, I can tell you immediately what the factors of numbers like 6 and 15 are. 72 still takes some thinking, though.

stingraycharles 5y ago

> you won't do the long division in your head, so clearly, you'll have to memorise I think this assumption is false; at least for me, doing these types of divisions in my head is doable, I think we actually had to be able to do these types of calculations mentally in elementary school. Eg in your examples you say 72/2 = 36, so then 72/4 must be 18. I think the number 72 was chosen specifically for this property, that it divides easily for common values of interest rate (1, 2, 3, 4, 6, 8, 9 all divide cleanly).

reedf1 5y ago

It's already an approximation - you do not need to get precise with your division. Also - you should be able to do 72 divided by at least 2,3,4 (and estimate it for others), even by times tables/estimation and not long division.

deleted 5y ago

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