Some help with percentages…
Discussion
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.
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.
Percentage means hundredth parts, the cent bit being the same as in a century or 100 years.
To work them out does take division unfortunately, in your case you want to know how much larger £200k is than £100k so all you do is divide the new value minus the original by the original value-
(200 - 100)/100 = 1 you can ignore the 'k' as it cancels out
To make it a percentage you multiply by 100, therefore in this case the new value is 100% larger than the original.
Now your original value just happened to be £100k, however if you had started with £120k and the value was now £192k the calculation would look like this.
(192 - 120)/120
72/120 = 0.6
As a percentage 0.6 x 100 = 60%, i.e. 192k is 60% larger than 120k
That is all a percentage is, a ratio multiplied by 100
To work them out does take division unfortunately, in your case you want to know how much larger £200k is than £100k so all you do is divide the new value minus the original by the original value-
(200 - 100)/100 = 1 you can ignore the 'k' as it cancels out
To make it a percentage you multiply by 100, therefore in this case the new value is 100% larger than the original.
Now your original value just happened to be £100k, however if you had started with £120k and the value was now £192k the calculation would look like this.
(192 - 120)/120
72/120 = 0.6
As a percentage 0.6 x 100 = 60%, i.e. 192k is 60% larger than 120k
That is all a percentage is, a ratio multiplied by 100
Ahhh ok, I’m seeing where I was going wrong, I thought a percentage was a multiple of something rather than a ratio, so I was missing the point, as an example, when I see 10% off, my abysmal maths would struggle trying to work out the 10%. If I’m right in my thinking now I’ve read your post, 10% or 5% or 8% are “hundredths” of the original number, so 8% off a £10 item would be 80 pence.
Apologies if it sounds like explaining stuff to a 5 year old, but my maths is really that bad.
Thanks for taking the time to explain that to me so clearly . I’m actually ok with fractions but rubbish with percentages and I could never get a handle on what is , in reality, a fairly simple concept.
Apologies if it sounds like explaining stuff to a 5 year old, but my maths is really that bad.
Thanks for taking the time to explain that to me so clearly . I’m actually ok with fractions but rubbish with percentages and I could never get a handle on what is , in reality, a fairly simple concept.
That is correct, lots of people have issues with what a percentage is and it is really a way to make a ratio simple.
With money you can do the divide by 100 simply changing £ to p then multiplying by the %age, as you did above.
8% of £10 is 8 x 10p = 80p
It is a bit more complicated if you are told something has gone up 20% and you want to know the original value, you would need to divide the value by the % so
144/1.2 = 120 or to get back 120 + 20% = 144, it is not 144 - 20% of 144 as hat would be 144 - 28.8 = 114.2, clearly wrong.
It can be easier to do this to start with the whole hundredths thing so you are dividing with whole numbers.
144 x (100/120), then 144 x (10/12), then 10 x (144/12) = 10 x 12 = 120
Bear in mind that something can expressed as being 20% larger or 120% of the original which are both the same thing. It is quite common for news items to say something has gone up to 250% of the original value, in which case it is 2.5 times or say it has increased by 150%, which is the same thing.
Apologies if I am overdoing it there, just wanted to make sure you don't get caught out by some of the common mistakes.
With money you can do the divide by 100 simply changing £ to p then multiplying by the %age, as you did above.
8% of £10 is 8 x 10p = 80p
It is a bit more complicated if you are told something has gone up 20% and you want to know the original value, you would need to divide the value by the % so
144/1.2 = 120 or to get back 120 + 20% = 144, it is not 144 - 20% of 144 as hat would be 144 - 28.8 = 114.2, clearly wrong.
It can be easier to do this to start with the whole hundredths thing so you are dividing with whole numbers.
144 x (100/120), then 144 x (10/12), then 10 x (144/12) = 10 x 12 = 120
Bear in mind that something can expressed as being 20% larger or 120% of the original which are both the same thing. It is quite common for news items to say something has gone up to 250% of the original value, in which case it is 2.5 times or say it has increased by 150%, which is the same thing.
Apologies if I am overdoing it there, just wanted to make sure you don't get caught out by some of the common mistakes.
texaxile said:
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?.
To answer your initial question, the 100k house purchased 20 years ago has increased by roughly 3.5% per annum based on monthly compound interest.Try this online calculator
https://www.thecalculatorsite.com/finance/calculat...
And yes, you can work out decreases as well as increases.
Mammasaid said:
To answer your initial question, the 100k house purchased 20 years ago has increased by roughly 3.5% per annum based on monthly compound interest.
Try this online calculator
https://www.thecalculatorsite.com/finance/calculat...
And yes, you can work out decreases as well as increases.
Doh, I missed the per year bit...Try this online calculator
https://www.thecalculatorsite.com/finance/calculat...
And yes, you can work out decreases as well as increases.
It was more the not being able to do a percentage calc i saw.
Toltec said:
That is correct, lots of people have issues with what a percentage is and it is really a way to make a ratio simple.
With money you can do the divide by 100 simply changing £ to p then multiplying by the %age, as you did above.
8% of £10 is 8 x 10p = 80p
It is a bit more complicated if you are told something has gone up 20% and you want to know the original value, you would need to divide the value by the % so
144/1.2 = 120 or to get back 120 + 20% = 144, it is not 144 - 20% of 144 as hat would be 144 - 28.8 = 114.2, clearly wrong.
It can be easier to do this to start with the whole hundredths thing so you are dividing with whole numbers.
144 x (100/120), then 144 x (10/12), then 10 x (144/12) = 10 x 12 = 120
Bear in mind that something can expressed as being 20% larger or 120% of the original which are both the same thing. It is quite common for news items to say something has gone up to 250% of the original value, in which case it is 2.5 times or say it has increased by 150%, which is the same thing.
Apologies if I am overdoing it there, just wanted to make sure you don't get caught out by some of the common mistakes.
I usually find that the easiest way to work out a price increase is:With money you can do the divide by 100 simply changing £ to p then multiplying by the %age, as you did above.
8% of £10 is 8 x 10p = 80p
It is a bit more complicated if you are told something has gone up 20% and you want to know the original value, you would need to divide the value by the % so
144/1.2 = 120 or to get back 120 + 20% = 144, it is not 144 - 20% of 144 as hat would be 144 - 28.8 = 114.2, clearly wrong.
It can be easier to do this to start with the whole hundredths thing so you are dividing with whole numbers.
144 x (100/120), then 144 x (10/12), then 10 x (144/12) = 10 x 12 = 120
Bear in mind that something can expressed as being 20% larger or 120% of the original which are both the same thing. It is quite common for news items to say something has gone up to 250% of the original value, in which case it is 2.5 times or say it has increased by 150%, which is the same thing.
Apologies if I am overdoing it there, just wanted to make sure you don't get caught out by some of the common mistakes.
Final Value * (1/(1+(Percentage value as a decimal))
In your example, that would be:
144 * 1/1+0.2
144 * 1/1.2
144 * 0.8333 (rec)
120
texaxile said:
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?.
As a couple of people have realised, if you really want the yearly increase (CAGR - Compound Anniual Growth Rate) it is pretty tricky - so don't beat yourself up. It can be done with a formula but generally these days you'd Google a suitable online calcualator, like the one another poster linked to, or this one does CAGR by putting start and finish amounts, and number of years: https://www.omnicalculator.com/finance/cagrtexaxile said:
Hi,
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?.
This is quite tricky, but luckily there's a very easy shortcut. Basically, your house has doubled in value over 20 years, so that's a 100% increase. Simple maths leads you divide the 100% by 20 years to give you a figure of 5% per year. But this is of course wrong, because in 2004 it would have been worth £105K, but in 2005 it wouldn't be worth £110K, but £110,250 . If you keep on adding 5% year on year (compound interest), your house would be worth way more than £200K. So we know it's less than 5%. But how to work it out? 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?.
That's where the rule of 72 helps. 72 is a magic number in the world of interest rates, and can quickly let you know what's the best deal when you have money to invest or need to borrow money.
Your £100K has gone up 100% in 20 years. If you'd invested £100K, and taken the interest out and spent it every year, and after 20 years you still had £100K invested but you'd also spent £100K, then dividing the 100 by 20 would give you 5%. That's what you earnt per year. But if you invested £100K (which you did when you bought your house), never spent any of it, and after 20 years you have £200K (which you do with your house value), instead of dividing the 100 by 20, divide 72 by 20 instead. This gives you 3.6, and £100K invested at 3.6% compounded gives you, within a few quid, £200K. So your house has increased in value by approx 3.6%/year.
Edited by TwigtheWonderkid on Monday 28th August 16:16
^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.
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
One issue when trying to grasp percentages is when it gets expressed as a formula. When I met them at school everything was multiplied by 'a hundred over one' which meant nothing to me. Now that I understand the actual concept behind percentages, I just divide one number by another and multiply it by 100. The trick is in knowing which number to divide.
One little gotcha is knowing which side to work from. For example, if you add 20% to 100 you get 120. But if you multiply 120 by 0.8 in a vain attempt to remove the 20% you only get 96 - because you had the wrong starting point.
I was able to teach percentages to a child by using the concept of a Twix bar cut into 100 slices. Then she suddenly understood how it worked. I like visual methods; in fact I still use mental Cuisenaire rods to add and subtract. They are easier to use than to spell
One little gotcha is knowing which side to work from. For example, if you add 20% to 100 you get 120. But if you multiply 120 by 0.8 in a vain attempt to remove the 20% you only get 96 - because you had the wrong starting point.
I was able to teach percentages to a child by using the concept of a Twix bar cut into 100 slices. Then she suddenly understood how it worked. I like visual methods; in fact I still use mental Cuisenaire rods to add and subtract. They are easier to use than to spell
Simpo Two said:
One little gotcha is knowing which side to work from. For example, if you add 20% to 100 you get 120. But if you multiply 120 by 0.8 in a vain attempt to remove the 20% you only get 96 - because you had the wrong starting point.
Also shows that a percentage loss is more than a percentage gain. If the value of something drops by, say, 20%, it requires a 25% increase in value to get back to where it was.V8LM said:
Simpo Two said:
One little gotcha is knowing which side to work from. For example, if you add 20% to 100 you get 120. But if you multiply 120 by 0.8 in a vain attempt to remove the 20% you only get 96 - because you had the wrong starting point.
Also shows that a percentage loss is more than a percentage gain. If the value of something drops by, say, 20%, it requires a 25% increase in value to get back to where it was.Thanks so much for the helpful replies everyone.
I'm still slowly getting to grips with the % increase and decreases , and moving onto the value of an item if it's gone up by 20% how much the original item was, but it's not easy, plus I'm trying to do it without the aid of a calculator and on a notepad, so I can follow my train of thought and working out. I'm also using random numbers, just to make sure I've got a clear understanding, and I've found a couple of YT videos to help as well.
Many thanks also to Twig for the "shortcut" with the magic number of 72, which I've not yet tried to tackle but will in the fullness of time.
Luckily my useless maths gene didn't pass down to my kids, and when the homework came around, I left it to their Mum.
Great stuff, and cheers everyone.
I'm still slowly getting to grips with the % increase and decreases , and moving onto the value of an item if it's gone up by 20% how much the original item was, but it's not easy, plus I'm trying to do it without the aid of a calculator and on a notepad, so I can follow my train of thought and working out. I'm also using random numbers, just to make sure I've got a clear understanding, and I've found a couple of YT videos to help as well.
Many thanks also to Twig for the "shortcut" with the magic number of 72, which I've not yet tried to tackle but will in the fullness of time.
Luckily my useless maths gene didn't pass down to my kids, and when the homework came around, I left it to their Mum.
Great stuff, and cheers everyone.
texaxile said:
Many thanks also to Twig for the "shortcut" with the magic number of 72, which I've not yet tried to tackle but will in the fullness of time.
Once you master it, you will have a better understanding of percentages and finance than many supposedly numeral people. For example, I wrote this several years ago on a thread about payday loans:Pay day loans (borrow £100 on 20th to tide you over until you get paid on 30th, then pay back £120). Or short terms loans to get people thru Xmas. The APR on these loans is simply staggering, 1000s of %. Of course, the people they are aimed at are the poorest and often the most badly educated, so they don't understand APR or percentage in general. Even some people who are quite numerate struggle with APR and percentages.
For people who aren't numerate, borrowing £100 and paying £120 ten days later sounds ok. 20% rate. Of course it's not 20% at all, more like 5000% in APR terms.
So I think it's time we did away with APR and such, and made it law that all loans should be quoted on a time basis, using Rule 72.
72 is a kind of magical number in the world of compound interest. If you borrow £5k to buy a car, and the interest rate is 12% per year compound, if you divide the interest rate (12) into 72, it gives you 6. Coincidentally, if you never made any payments on the £5K/12% loan, the amount you owned would double in 6 yrs. So that loan, instead of being quoted at 12%, would be quoted as a Rule 72 six year loan.
Every loan firm would have to quote the Rule 72 time, the time it takes your loan to double if unpaid. Then even customers who were useless with figures would know that the longer the time, the better the loan. A loan that doubles in 7 yrs is better than a loan that doubles in 6.
Take my original payday loan. 20% interest for 10 days. Divide 20 into 72 gives you 3.6. Then multiply the 10 days by 3.6 to give 36 days. So that would be a Rule 72 36 day loan. The £100 you borrowed would turn into £200 owed in 36 days. And £400 36 days after that.
Anyone can see that a Rule 72 36 day loan is terrible compared to a Rule 72 6 year loan, which is what they might be offered on a personal car finance plan.
A mortgage might have an annual rate of 3.25% for example. 72 divided by 3.25 is 22.15. So a mortgage for £150K at 3.25% per annum would double to £300K in 22.15 years, if you never made any payments.
That's my theory. Hope I've explained it properly. No more apr or % rate. Just Rule 72 time period. It works in reverse too.
If you have money to invest, and someone was offering 6% per year, they wouldn't quote 6% under my system, they'd say our Rule 72 time is 12 years. If you invest your money with us, it'll take you 12 yrs to double your money if you don't touch it. Because paying 6%, you have to multiply that by 12 to get 72. Try it on a calculator with 100, and add 6% 12 times, and it comes to £201.21. The rule works, within a couple of quid either way, for any amount, over any period.
On a savings account, the shorter the Rule 72 time the better, a saving account that doubles your money in 12 years is better than one that takes 13 years. Anyone can understand that, regardless of how poor they are with numbers and maths.
72...a magic number in the world of compound interest.
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.
People who can't read and write well are ashamed of the fact (they shouldn't be) and do everything they can to hide the fact. But if you're bad at maths in Britain, it's something to boast and laugh about. I've got a family member who wouldn't have a clue how to add 10% to 100 and is seemingly proud of it, and it happy to laugh about how bad at maths she is. She'll share this fact with anyone prepared to listen.
It's great when grown adults who aren't good at maths make a decision to actually try and get better. Most local authorities councils run adult numeracy classes but struggle to fill them. They fill the adult literacy classes no problem (often with immigrants committed to improving their English).
People who can't read and write well are ashamed of the fact (they shouldn't be) and do everything they can to hide the fact. But if you're bad at maths in Britain, it's something to boast and laugh about. I've got a family member who wouldn't have a clue how to add 10% to 100 and is seemingly proud of it, and it happy to laugh about how bad at maths she is. She'll share this fact with anyone prepared to listen.
It's great when grown adults who aren't good at maths make a decision to actually try and get better. Most local authorities councils run adult numeracy classes but struggle to fill them. They fill the adult literacy classes no problem (often with immigrants committed to improving their English).
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?
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