Some help with percentages…
Discussion
Ash_ said:
Twig, may I ask where the 72 number is/was derived from? How did we get to understand that "72" is the magic number? Does it relate to repayment months or an average % over a year.....how did we get to 72 being able to be used to help in such calculations.....or is it literally magic?
It's been around for over 500 years. It works for interest compounding year on year. For interest that compounds daily, swap 72 for 69 for a more accurate result. But basically, 72 will always give you a reasonably accurate answer. From the internet:
History
An early reference to the rule is in the Summa de arithmetica (Venice, 1494. Fol. 181, n. 44) of Luca Pacioli (1445–1514). He presents the rule in a discussion regarding the estimation of the doubling time of an investment, but does not derive or explain the rule, and it is thus assumed that the rule predates Pacioli by some time.
A voler sapere ogni quantità a tanto per 100 l'anno, in quanti anni sarà tornata doppia tra utile e capitale, tieni per regola 72, a mente, il quale sempre partirai per l'interesse, e quello che ne viene, in tanti anni sarà raddoppiato. Esempio: Quando l'interesse è a 6 per 100 l'anno, dico che si parta 72 per 6; ne vien 12, e in 12 anni sarà raddoppiato il capitale. (emphasis added).
Roughly translated:
In wanting to know of any capital, at a given yearly percentage, in how many years it will double adding the interest to the capital, keep as a rule [the number] 72 in mind, which you will always divide by the interest, and what results, in that many years it will be doubled. Example: When the interest is 6 percent per year, I say that one divides 72 by 6; 12 results, and in 12 years the capital will be doubled.
Edited by TwigtheWonderkid on Wednesday 30th August 12:49
Edited by TwigtheWonderkid on Wednesday 30th August 12:50
TwigtheWonderkid said:
One other thing. Well done to the OP for admitting his maths is bad (not uncommon) and wanting to do something about it (incredibly uncommon). The standards of maths in the UK is dreadful, but for some reason, people are happy to admit to it, and joke about it. It's almost a badge of honour to be crap at maths.
When I was at university I had to integrate partial fractions in my head. Even then percentages were a mystery to me. Some things just clicked when I was learning whilst others seemed like a deep, dark abyss. These days, I'm not entirely sure I could say what a partial fraction is without looking it up.That rule of 72 is brilliant though. Thanks for that.
TwigtheWonderkid said:
It's been around for over 500 years. It works for interest compounding year on year. For interest that compounds daily, swap 72 for 69 for a more accurate result. But basically, 72 will always give you a reasonably accurate answer.
From the internet:
History
An early reference to the rule is in the Summa de arithmetica (Venice, 1494. Fol. 181, n. 44) of Luca Pacioli (1445–1514). He presents the rule in a discussion regarding the estimation of the doubling time of an investment, but does not derive or explain the rule, and it is thus assumed that the rule predates Pacioli by some time.
A voler sapere ogni quantità a tanto per 100 l'anno, in quanti anni sarà tornata doppia tra utile e capitale, tieni per regola 72, a mente, il quale sempre partirai per l'interesse, e quello che ne viene, in tanti anni sarà raddoppiato. Esempio: Quando l'interesse è a 6 per 100 l'anno, dico che si parta 72 per 6; ne vien 12, e in 12 anni sarà raddoppiato il capitale. (emphasis added).
Roughly translated:
In wanting to know of any capital, at a given yearly percentage, in how many years it will double adding the interest to the capital, keep as a rule [the number] 72 in mind, which you will always divide by the interest, and what results, in that many years it will be doubled. Example: When the interest is 6 percent per year, I say that one divides 72 by 6; 12 results, and in 12 years the capital will be doubled.
From the internet:
History
An early reference to the rule is in the Summa de arithmetica (Venice, 1494. Fol. 181, n. 44) of Luca Pacioli (1445–1514). He presents the rule in a discussion regarding the estimation of the doubling time of an investment, but does not derive or explain the rule, and it is thus assumed that the rule predates Pacioli by some time.
A voler sapere ogni quantità a tanto per 100 l'anno, in quanti anni sarà tornata doppia tra utile e capitale, tieni per regola 72, a mente, il quale sempre partirai per l'interesse, e quello che ne viene, in tanti anni sarà raddoppiato. Esempio: Quando l'interesse è a 6 per 100 l'anno, dico che si parta 72 per 6; ne vien 12, e in 12 anni sarà raddoppiato il capitale. (emphasis added).
Roughly translated:
In wanting to know of any capital, at a given yearly percentage, in how many years it will double adding the interest to the capital, keep as a rule [the number] 72 in mind, which you will always divide by the interest, and what results, in that many years it will be doubled. Example: When the interest is 6 percent per year, I say that one divides 72 by 6; 12 results, and in 12 years the capital will be doubled.
Edited by TwigtheWonderkid on Wednesday 30th August 12:49
That's really worth its weight in gold. The Mrs is very good at numbers, I've shown her this entire thread because she sympathises with my lack of skills in all things numerical, and in her words Mr Twig, you deserve a "good number of beers".
I'm perfectly ok with fractions.One thing I cannot get my head around is 1/3 as a percentage. I understand it works out at 33%, but 3 thirds = 1 whole, whereas 3x 33% = 99%. I don;t want to get too deep into this, as my brain might overload...
looking at a pie chart (which is how I visualise numbers / fractions) from a fractional aspect it is easy, but from a percentage aspect there's always something left over. For the life of me I cannot understand why that is the case.
Edited by texaxile on Saturday 2nd September 23:24
texaxile said:
Edited by TwigtheWonderkid on Wednesday 30th August 12:49
That's really worth its weight in gold. The Mrs is very good at numbers, I've shown her this entire thread because she sympathises with my lack of skills in all things numerical, and in her words Mr Twig, you deserve a "good number of beers".
I'm perfectly ok with fractions.One thing I cannot get my head around is 1/3 as a percentage. I understand it works out at 33%, but 3 thirds = 1 whole, whereas 3x 33% = 99%. I don;t want to get too deep into this, as my brain might overload...
looking at a pie chart (which is how I visualise numbers / fractions) from a fractional aspect it is easy, but from a percentage aspect there's always something left over. For the life of me I cannot understand why that is the case.
Edited by texaxile on Saturday 2nd September 23:24
But add some decimal points and it is 33.333333333%
Basically, that extra 1 you couldn’t understand also needs to be divided by 3.
As in 33.333333/100
Don’t beat yourself up about it too much, doing sums like this in your head is good for approximation.
Anything that needs a more precise answer, the majority ( more than 50%) would probably do it using a calculator or online or in Excel….
Cupid-stunt said:
As a whole number, yes it is 33%.
But add some decimal points and it is 33.333333333%
Basically, that extra 1 you couldn’t understand also needs to be divided by 3.
As in 33.333333/100
Don’t beat yourself up about it too much, doing sums like this in your head is good for approximation.
Anything that needs a more precise answer, the majority ( more than 50%) would probably do it using a calculator or online or in Excel….
Right, I see now. I'm over thinking that particular aspect way too much, and as you say, for an approximation it works fine.But add some decimal points and it is 33.333333333%
Basically, that extra 1 you couldn’t understand also needs to be divided by 3.
As in 33.333333/100
Don’t beat yourself up about it too much, doing sums like this in your head is good for approximation.
Anything that needs a more precise answer, the majority ( more than 50%) would probably do it using a calculator or online or in Excel….
V8LM said:
^very clever^
The long way is (assuming the annual percentage increase is constant) (taking thousands below):
In 2003, house was worth 100
In 2004, house was worth 100 * inc
In 2005, house was worth 100 * inc * inc
In 2006, house was worth 100 * inc * inc * inc
etc...
After y years, the house is worth 100*inc^y (^ is power)
If after 20 years, the house is worth 200, then
100*inc^20 = 200
inc^20 = 200 / 100
inc^20 = 2
To find inc, we can convert from a linear scale of 0, 1, 2, 3, ..., to a logarithmic scale, such as 1, 10, 100, 1000, ... This scale is logarithms to the base 10 (although any base will do). In this scale, every number is a multiple of the previous.
Convert both sides to logs
log(inc^20) = log(2)
inc^20 converted to logs, where every number is a multiple of the previous, is equal to 20 * log(inc)
20 log(inc) = log(2)
log(inc) = log(2) / 20
log(inc) = 0.015
We then convert back to our linear scale
inc = 10^0.015
inc = 1.035
Each year, the house is worth 1.035 times what it was the year before.
1.035 is a 3.5% increase.
Just what Twig said.
Easier still:The long way is (assuming the annual percentage increase is constant) (taking thousands below):
In 2003, house was worth 100
In 2004, house was worth 100 * inc
In 2005, house was worth 100 * inc * inc
In 2006, house was worth 100 * inc * inc * inc
etc...
After y years, the house is worth 100*inc^y (^ is power)
If after 20 years, the house is worth 200, then
100*inc^20 = 200
inc^20 = 200 / 100
inc^20 = 2
To find inc, we can convert from a linear scale of 0, 1, 2, 3, ..., to a logarithmic scale, such as 1, 10, 100, 1000, ... This scale is logarithms to the base 10 (although any base will do). In this scale, every number is a multiple of the previous.
Convert both sides to logs
log(inc^20) = log(2)
inc^20 converted to logs, where every number is a multiple of the previous, is equal to 20 * log(inc)
20 log(inc) = log(2)
log(inc) = log(2) / 20
log(inc) = 0.015
We then convert back to our linear scale
inc = 10^0.015
inc = 1.035
Each year, the house is worth 1.035 times what it was the year before.
1.035 is a 3.5% increase.
Just what Twig said.
Edited by V8LM on Monday 28th August 21:50
If 100*x^20=200
Then x = 20th root of 200/100
texaxile said:
I'm perfectly ok with fractions.One thing I cannot get my head around is 1/3 as a percentage. I understand it works out at 33%, but 3 thirds = 1 whole, whereas 3x 33% = 99%. I don;t want to get too deep into this, as my brain might overload...
looking at a pie chart (which is how I visualise numbers / fractions) from a fractional aspect it is easy, but from a percentage aspect there's always something left over. For the life of me I cannot understand why that is the case.
Because 100 isn't divisible by 3, that's all.looking at a pie chart (which is how I visualise numbers / fractions) from a fractional aspect it is easy, but from a percentage aspect there's always something left over. For the life of me I cannot understand why that is the case.
OP, with a bit of work, you'll soon be making important decisions, lifechanging choices, based on your new found skillset.
For example, someone posted on Twitter that Domino’s charge £5.99 for a cheesy garlic bread side order, which is six inches in diameter, which is 28.26 square inches of cheesy garlic bread, working out at 21p per square inch.
You can also create your own small (9.5 inches in diameter) pizza for £8, and you can remove the tomato sauce, and then add garlic spread and mozzarella while keeping the thick crust, which is 70.85 square inches of cheesy garlic bread, working out at 11p per square inch - this is basically half the price per square inch. You’re paying £2.01 more (33%), but you’re getting 150.7% more cheesy garlic bread.
If you’re feeding a few people or whatever, creating your own cheesy garlic bread becomes an even better proposition. At the moment, any medium pizza (11.5 inches) is £10, which is 102.5 square inches of cheesy garlic bread, which is 10p per square inch. Any large pizza (13.5 inches) is £12, which is 143.07 square inches of cheesy garlic bread, which is 8p per square inch.
Whichever way you look at it, it simply doesn’t pay to order one or more of the regular cheesy garlic bread sides.
I’m working with pi being 3.14 and rounding to two decimal places elsewhere, and using ‘delivery’ prices only, and as you can see the end product is basically the same thing. I’m going by the prices at my local branch, and these could vary across the UK, but the concept itself that creating your own garlic bread beats the standard menu one should remain.
For example, someone posted on Twitter that Domino’s charge £5.99 for a cheesy garlic bread side order, which is six inches in diameter, which is 28.26 square inches of cheesy garlic bread, working out at 21p per square inch.
You can also create your own small (9.5 inches in diameter) pizza for £8, and you can remove the tomato sauce, and then add garlic spread and mozzarella while keeping the thick crust, which is 70.85 square inches of cheesy garlic bread, working out at 11p per square inch - this is basically half the price per square inch. You’re paying £2.01 more (33%), but you’re getting 150.7% more cheesy garlic bread.
If you’re feeding a few people or whatever, creating your own cheesy garlic bread becomes an even better proposition. At the moment, any medium pizza (11.5 inches) is £10, which is 102.5 square inches of cheesy garlic bread, which is 10p per square inch. Any large pizza (13.5 inches) is £12, which is 143.07 square inches of cheesy garlic bread, which is 8p per square inch.
Whichever way you look at it, it simply doesn’t pay to order one or more of the regular cheesy garlic bread sides.
I’m working with pi being 3.14 and rounding to two decimal places elsewhere, and using ‘delivery’ prices only, and as you can see the end product is basically the same thing. I’m going by the prices at my local branch, and these could vary across the UK, but the concept itself that creating your own garlic bread beats the standard menu one should remain.
texaxile said:
Hi,
My maths is shockingly bad. When I tell you that I can’t divide or do anything other than simple division, same goes for multiplication. Addition and subtraction I can do, but in order to subtract I need to count up from the number being subtracted, or just give up and use the phone.
I’m looking for help when I try to work out the percentage something has increased in value over a number of years.
For example as follows:
Say we purchased a house in 2003 for 100k. Today it’s valued at 200k, is there a formula I can use to work out how much, by percentage it has increased yearly?. How would I go about doing it, and can the same method be used to work out a decrease in value or amounts?.
I’m so useless I can’t even Google search it, as I’m really not able to explain in the search bar what it is I’m after.
Also, is there anywhere I can start off with basic maths and build up to being able to do the …basics?. A simple online source that I can maybe use during tea breaks little and often?.
Thanks in advance people, and a virtual single malt to you all.
Mods, apologies if this is in the wrong sub forum.
BBC used to do GCSE bite sizes for maths etc. which were supposed to be good. My maths is shockingly bad. When I tell you that I can’t divide or do anything other than simple division, same goes for multiplication. Addition and subtraction I can do, but in order to subtract I need to count up from the number being subtracted, or just give up and use the phone.
I’m looking for help when I try to work out the percentage something has increased in value over a number of years.
For example as follows:
Say we purchased a house in 2003 for 100k. Today it’s valued at 200k, is there a formula I can use to work out how much, by percentage it has increased yearly?. How would I go about doing it, and can the same method be used to work out a decrease in value or amounts?.
I’m so useless I can’t even Google search it, as I’m really not able to explain in the search bar what it is I’m after.
Also, is there anywhere I can start off with basic maths and build up to being able to do the …basics?. A simple online source that I can maybe use during tea breaks little and often?.
Thanks in advance people, and a virtual single malt to you all.
Mods, apologies if this is in the wrong sub forum.
Set yourself a target perhaps to learn/do a maths GCSE and that’s a good way to learn towards a goal.
Great job on making an effort to close out something you feel you need to improve on, it’s never too late
TwigtheWonderkid said:
For example, someone posted on Twitter that Domino’s charge £5.99 for a cheesy garlic bread side order, which is six inches in diameter, which is 28.26 square inches of cheesy garlic bread, working out at 21p per square inch.
I once worked out the price per unit area of the three sizes of pizza that my local takeaway offered - and they were exactly the same! So someone there can do pi r squared!However, if the width of topping-less edge is the same on all three sizes, then you'd get better value (more topping pro rata) with the largest size. Same concept as surface area to volume ratio but minus a dimension...
NRG1976 said:
Great job on making an effort to close out something you feel you need to improve on, it’s never too late
Presume 'close out' is newspeak for 'learn', as 'reach out' is for 'ask'?Edited by Simpo Two on Monday 11th September 14:57
Simpo Two said:
TwigtheWonderkid said:
For example, someone posted on Twitter that Domino’s charge £5.99 for a cheesy garlic bread side order, which is six inches in diameter, which is 28.26 square inches of cheesy garlic bread, working out at 21p per square inch.
I once worked out the price per unit area of the three sizes of pizza that my local takeaway offered - and they were exactly the same! So someone there can do pi r squared!However, if the width of topping-less edge is the same on all three sizes, then you'd get better value (more topping pro rata) with the largest size. Same concept as surface area to volume ratio but minus a dimension...
NRG1976 said:
Great job on making an effort to close out something you feel you need to improve on, it’s never too late
Presume 'close out' is newspeak for 'learn', as 'reach out' is for 'ask'?Edited by Simpo Two on Monday 11th September 14:57
NRG1976 said:
May well be, I just see a skill that is missing as a gap that needs to be closed out. That said, I do suffer from corporate vocabulary issues, so perhaps I can circle back with you and confirm later? Inbox me if I forget.
Nice bit of blue sky thinking. Let's put it in the saucer and see if the cat laps it up. NRG1976 said:
May well be, I just see a skill that is missing as a gap that needs to be closed out. That said, I do suffer from corporate vocabulary issues, so perhaps I can circle back with you and confirm later? Inbox me if I forget.
Gaps are usually filled. Have a scuba in your think-tank and see if you can downsize your sloppiness overload 
TwigtheWonderkid said:
OP, with a bit of work, you'll soon be making important decisions, lifechanging choices, based on your new found skillset.
For example, someone posted on Twitter that Domino’s charge £5.99 for a cheesy garlic bread side order, which is six inches in diameter, which is 28.26 square inches of cheesy garlic bread, working out at 21p per square inch.
You can also create your own small (9.5 inches in diameter) pizza for £8, and you can remove the tomato sauce, and then add garlic spread and mozzarella while keeping the thick crust, which is 70.85 square inches of cheesy garlic bread, working out at 11p per square inch - this is basically half the price per square inch. You’re paying £2.01 more (33%), but you’re getting 150.7% more cheesy garlic bread.
If you’re feeding a few people or whatever, creating your own cheesy garlic bread becomes an even better proposition. At the moment, any medium pizza (11.5 inches) is £10, which is 102.5 square inches of cheesy garlic bread, which is 10p per square inch. Any large pizza (13.5 inches) is £12, which is 143.07 square inches of cheesy garlic bread, which is 8p per square inch.
Whichever way you look at it, it simply doesn’t pay to order one or more of the regular cheesy garlic bread sides.
I’m working with pi being 3.14 and rounding to two decimal places elsewhere, and using ‘delivery’ prices only, and as you can see the end product is basically the same thing. I’m going by the prices at my local branch, and these could vary across the UK, but the concept itself that creating your own garlic bread beats the standard menu one should remain.
For example, someone posted on Twitter that Domino’s charge £5.99 for a cheesy garlic bread side order, which is six inches in diameter, which is 28.26 square inches of cheesy garlic bread, working out at 21p per square inch.
You can also create your own small (9.5 inches in diameter) pizza for £8, and you can remove the tomato sauce, and then add garlic spread and mozzarella while keeping the thick crust, which is 70.85 square inches of cheesy garlic bread, working out at 11p per square inch - this is basically half the price per square inch. You’re paying £2.01 more (33%), but you’re getting 150.7% more cheesy garlic bread.
If you’re feeding a few people or whatever, creating your own cheesy garlic bread becomes an even better proposition. At the moment, any medium pizza (11.5 inches) is £10, which is 102.5 square inches of cheesy garlic bread, which is 10p per square inch. Any large pizza (13.5 inches) is £12, which is 143.07 square inches of cheesy garlic bread, which is 8p per square inch.
Whichever way you look at it, it simply doesn’t pay to order one or more of the regular cheesy garlic bread sides.
I’m working with pi being 3.14 and rounding to two decimal places elsewhere, and using ‘delivery’ prices only, and as you can see the end product is basically the same thing. I’m going by the prices at my local branch, and these could vary across the UK, but the concept itself that creating your own garlic bread beats the standard menu one should remain.
That’s obviously very clear and easy to understand, but you haven’t factored in wifey’s blue light discount….
50%…
Dammit.
Gassing Station | Science! | Top of Page | What's New | My Stuff