7.0% actually 3.69%?

zagfles

anakeimai said:

Apologies if I caused offence - I'm obviously not as informed as the Sunday Times (see: newbie), and clearly wasn't aware (actually, baffled) about the sensitive politics on here...  

There is no "sensitive politics" here, just a mix of people with a wide variety of opinions. Some may think those who don't understand the way interest works are thick, some may think anyone who understands it well is a boring geek, some enjoy discussing pedantic detail, some just like a good argument.

I've asked loads of questions on online forums on subjects I don't understand well, you always get those who make you feel stupid, you always get those who divert the thread onto unrelated topics, but you also get useful answers in amongst it all. I'd far rather a thread where my question is answered several times over by different people in different ways even with an "aren't you stupid" air to them than get no answers at all.

CooperSF

Johnjdc said:

What needs explaining?

You are calculating based on 7% of £3600, but you aren't saving £3,600 for a year, because you are paying it in gradually

No bank will pay you 12 months' interest for money you only save with them for one month. Why would they?

A little rude.

Let's treat forum users with some respect please.

zagfles

AmityNeon said:

zagfles said:

AmityNeon said:

zagfles said:

Beddie said:

Millyonare said:

The UK should really make all pupils 14-16yo do a GCSE in Arithmetic -- and not leave school until they achieve grade 4 / C or better.

For the vast majority of employees and employers, simple arithmetic is all the maths they will mostly ever need to use in work or home or for personal finances.

Mandatory GCSE Arithmetic would noticeably improve UK productivity.

I get your point, but not everyone is capable of being good at arithmetic. In the same way I cannot draw or paint, others cannot work with numbers. And just forcing them will put them off for life. There should be plenty of encouraging, yes, and also schools should do realistic scenarios e.g. wages, tax, renting, buying a house etc. instead of the "dry" maths mostly taught. Have it as a project, not just a lesson.

Yes, stuff like algebra is a good example. It can be used for all sorts of useful things, I've just used it to work out how much I should be spending on my Barclaycard to get best value from the balance transfer I've just done. But most people just learn it at school then forget about it because they don't see the practical use for it, because it was never taught in the context of real life scenarios.

Basic algebra is wonderfully applicable as it only requires logic. Recently we wanted to determine whether it was worth 'renewing' LBG Regular Savers to their higher rates, which resulted in generic formulas. Simplifying can take a bit of arithmetic training and perhaps an affinity for numbers, but simplifying isn't strictly necessary with calculators doing the heavy lifting.

Not sure about only logic, you do need a bit of arithmetric training. Rearranging an equation is usually as hard or harder than "simplifying", and you can't use a (normal) calculator for that, and you do need to rearrange when the value you're resolving for is on both sides of the equation. That doesn't seem to be the case with your regular saver formula, so although it looks complicated it is probably simpler in that the value you are calculating is only on one side of the formula, so no rearranging is necessary.

Basic rearranging only requires an elementary understanding of arithmetic, and the rest is logic; if an operation is performed on one side of an equation, it must also be performed on the other for logical consistency. Simplifying a more complicated formula often requires expansion and factoring, which I wouldn't expect the average person to easily perform unless they were already doing so somewhat regularly in their daily life (e.g. when studying or working).

The full formula was:

mrn(n+1)/24 + m(r+x)(12-n)(12-n+1)/24 + m(r-y)n(12-n)/12 > mr6.5

The necessary values (monthly contribution, number of months, and the three interest rates) can be plugged into a calculator/spreadsheet for the desired result, i.e. to determine whether the left side generates more interest than the right.

It simplifies (eliminating the unnecessary m and r) to:

(n − 12) * [(n − 13) * x + (2 * n * y)] > 0

It's not mostly logic though. Perform the "same operation" on both sides? Very logical. But you need to understand that you need to perform the same operation on every element if it's a multiplication, but not if it's addition etc.

eg a + b = c

ax + bx = cx   (every element multiplied by x)

But

a + b + x = c + x   (not a+x + b+x = c+x)

Or for instance

1/x + 1/y = 1/z

Same operation on each element? OK put each element to the power of -1

So x + y = z

Wrong.

There's a lot of arithmetical rules you need to understand to do even the most basic algebra, rules that you probably take for granted as you know them well. It's not just or even mostly logic.

zagfles

ForumUser7 said:

zagfles said:

AmityNeon said:

zagfles said:

AmityNeon said:

zagfles said:

Beddie said:

Millyonare said:

The UK should really make all pupils 14-16yo do a GCSE in Arithmetic -- and not leave school until they achieve grade 4 / C or better.

For the vast majority of employees and employers, simple arithmetic is all the maths they will mostly ever need to use in work or home or for personal finances.

Mandatory GCSE Arithmetic would noticeably improve UK productivity.

I get your point, but not everyone is capable of being good at arithmetic. In the same way I cannot draw or paint, others cannot work with numbers. And just forcing them will put them off for life. There should be plenty of encouraging, yes, and also schools should do realistic scenarios e.g. wages, tax, renting, buying a house etc. instead of the "dry" maths mostly taught. Have it as a project, not just a lesson.

Yes, stuff like algebra is a good example. It can be used for all sorts of useful things, I've just used it to work out how much I should be spending on my Barclaycard to get best value from the balance transfer I've just done. But most people just learn it at school then forget about it because they don't see the practical use for it, because it was never taught in the context of real life scenarios.

Basic algebra is wonderfully applicable as it only requires logic. Recently we wanted to determine whether it was worth 'renewing' LBG Regular Savers to their higher rates, which resulted in generic formulas. Simplifying can take a bit of arithmetic training and perhaps an affinity for numbers, but simplifying isn't strictly necessary with calculators doing the heavy lifting.

Not sure about only logic, you do need a bit of arithmetric training. Rearranging an equation is usually as hard or harder than "simplifying", and you can't use a (normal) calculator for that, and you do need to rearrange when the value you're resolving for is on both sides of the equation. That doesn't seem to be the case with your regular saver formula, so although it looks complicated it is probably simpler in that the value you are calculating is only on one side of the formula, so no rearranging is necessary.

Basic rearranging only requires an elementary understanding of arithmetic, and the rest is logic; if an operation is performed on one side of an equation, it must also be performed on the other for logical consistency. Simplifying a more complicated formula often requires expansion and factoring, which I wouldn't expect the average person to easily perform unless they were already doing so somewhat regularly in their daily life (e.g. when studying or working).

The full formula was:

mrn(n+1)/24 + m(r+x)(12-n)(12-n+1)/24 + m(r-y)n(12-n)/12 > mr6.5

The necessary values (monthly contribution, number of months, and the three interest rates) can be plugged into a calculator/spreadsheet for the desired result, i.e. to determine whether the left side generates more interest than the right.

It simplifies (eliminating the unnecessary m and r) to:

(n − 12) * [(n − 13) * x + (2 * n * y)] > 0

It's not mostly logic though. Perform the "same operation" on both sides? Very logical. But you need to understand that you need to perform the same operation on every element if it's a multiplication, but not if it's addition etc.

eg a + b = c

ax + bx = cx   (every element multiplied by x)

But

a + b + x = c + x   (not a+x + b+x = c+x)

Or for instance

1/x + 1/y = 1/z

Same operation on each element? OK put each element to the power of -1

So x + y = z

Wrong.

There's a lot of arithmetical rules you need to understand to do even the most basic algebra, rules that you probably take for granted as you know them well. It's not just or even mostly logic.

Re 1/x + 1/y = 1/z

1/3 + 1/12 = 4/12 + 1/12 = 5/12
1/7 + 1/3 = 3/21 + 7/21 = 10/21

1/x + 1/y = y/(xy) + x/(yx) = (y+x)/(xy) which could be written as (y+x)/z, but I'm not sure re 1/z - I may be missing something, or it might be I've misinterpreted what you meant by it

Just that the "logic" of doing the same thing to each side/each element isn't always right.

For that one, if you resolve for z then as you've mostly done, (y+x)/xy = 1/z and so z = xy/(x+y)

Using "logic" you can actually prove that 1 = 2

xy = xz

Therefore y = z (same operation both sides, right?)

What if x is 0, y is 1, and z is 2.

xy = xz is true, both sides 0.

But logic above says that means y = z

so 1 = 2  

jaypers

Wish the mods would close this thread! 

zagfles

jaypers said:

Wish the mods would close this thread! 

Why? Just don't read it if you're not interested.

DiamondLil

jaypers said:

Wish the mods would close this thread! 

I'm actually learning something here !

AmityNeon

zagfles said:

AmityNeon said:

zagfles said:

Not sure about only logic, you do need a bit of arithmetric training. Rearranging an equation is usually as hard or harder than "simplifying", and you can't use a (normal) calculator for that, and you do need to rearrange when the value you're resolving for is on both sides of the equation. 

Basic rearranging only requires an elementary understanding of arithmetic, and the rest is logic; if an operation is performed on one side of an equation, it must also be performed on the other for logical consistency.

It's not mostly logic though. Perform the "same operation" on both sides? Very logical. But you need to understand that you need to perform the same operation on every element if it's a multiplication, but not if it's addition etc.

eg a + b = c

ax + bx = cx (every element multiplied by x)

But

a + b + x = c + x (not a+x + b+x = c+x)

The fundamentals of arithmetic are derived through the application of logic. It is not logical to add x twice on the left, but only once on the right.

Multiplication is derived from applying logic:

• x * (a + b) =
• x 'lots' of (a + b) =
• adding (a + b) to itself x number of times =
• ax + bx

These are not 'rules' a person has to learn from an external source; they can be intuitively deduced through logic, although the notation must be learnt so that the concepts can be effectively represented and communicated. As an extreme example, child prodigies are truly and naturally fascinating, not because they are born possessing a fountain of knowledge, but because of their neurological affinity and acuity.

zagfles said:

Just that the "logic" of doing the same thing to each side/each element isn't always right.

That's not mathematically logical; artistically consistent perhaps, but I wouldn't call it logic, because those symbols denote specific concepts derived from logic.

zagfles said:

Using "logic" you can actually prove that 1 = 2

xy = xz

Therefore y = z (same operation both sides, right?)

What if x is 0, y is 1, and z is 2.

xy = xz is true, both sides 0.

But logic above says that means y = z

so 1 = 2

y = z cannot be logically deduced from xy = xz if x = 0.

x being 0 means it logically nullifies anything y or z could represent, regardless of their individual values. Also, logically, you cannot split (divide) something by (or into) nothing.

Bridlington1

I appreciate we've veered rather off topic but it is not that often that mathematical logic comes up on this forum in quite so much depth as this so may I take the opportunity to throw the Monty Hall problem into the ring?

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others are goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? (we'll assume for this example that you don't want a goat)

One's instinct would be to say that since there is one car and one goat left, you must have either the car or the goat so the chances of you having the car behind door No. 1 is 1/2.

But this is not the case

At the start of the game you had a 1/3 chance of picking the car, the host will pick one of the remaining goats.

If you picked a goat (2/3 chance) the host will have revealed the location of the one remaining goat so door No. 2 will contain the car so long as door No. 1 contains a goat. If you switch you win the car. 

If you picked the car (1/3 chance) the host will have revealed the location of one of the goats, so door No. 2 will contain another goat. So if you switch you win a goat. 

Or to show it through shear brute force one could list the scenarios:

Behind door 1	Behind door 2	Behind door 3	Result if sticking with door 1	Result if switching to the other door
Goat	Goat	Car	Wins goat	Wins car
Goat	Car	Goat	Wins goat	Wins car
Car	Goat	Goat	Wins car	Wins goat

Hence in reality your chances of winning the car if you stick with No. 1 is actually only 1/3. Therefore it is advantageous to switch your choice.

Bringing all this back to the original points of this thread, whilst at first it seems logical that switching your choice of door will not have any impact on the chances of you winning the car, on closer inspection we see that you are far better off switching than sticking with your original choice. Your initial logic was in this case flawed and thus easily can deceive you.

In a similar vein, whilst it may seem logical that if you put £300/mth into a regular saver paying 7% your total interest would be 300x12x0.07, in reality upon closer inspection this logic, much like the original logic in the previous example, turns out to be flawed as well and you can deceive yourself as a result of your own logic.

In a nutshell mathematical problems are not always as simple as they may first appear and can yield some surprising results, particularly if you are not familiar with them. If you are familiar with these problems however the true solutions seem far more obvious than they were at first.

AmityNeon

If your 'logic' deceives you, you're not being logical.

It doesn't matter whether it's logical reasoning or mathematical logic; flawed logic is, by definition, flawed and illogical.