7.0% actually 3.69%?

zagfles

dcs34 said:

zagfles said:

Malthusian said:

zagfles said:

But you do get calculators telling you 1 + 2 x 3 = 9 when the correct answer is 7. Try the Windows calculator in standard mode, then try it in scientific mode.

Anyone with a C in IT will tell you that you asked the calculator what (1 + 2) x 3 is and it answered correctly. Not the computer's fault that your input wasn't the same as the question you wanted to ask.
You don't need to be Einstein to understand that the "standard mode" executes each operation as it goes along.

No, I asked 1 + 2 x 3. I used no brackets in my question.

The correct answer to the question I asked is 7. I asked both calculators the exact same question and got different answers. Anyone with a C in both IT and maths will tell you that the IT is rubbish as it doesn't understand the rules of maths. The answer to a simple sum like 1+2x3 isn't "well it depends if you're a scientist or not"

If you used the Microsoft Calculator on Standard Mode then you never actually asked it to compute 1 + 2 x 3. In standard mode it can only perform a single operation on each calculation line.

You asked it 1 + 2, which is immediately told you was 3 (correct).

You then multiplied that result (3) x 3, which it told you was 9 (correct).

You can argue it as a UI error, or a user error, but the actual maths was correct.

I asked it exactly what I asked the "scientific" calculator, or my old Casio calculator I've had since I was at school. They both get it right. My phone has the same concept of a standard calculator with just the basic operations and a scientific one with all sorts of other more advanced operations. But both tell me that 1 + 2 x 3 = 7.

There's only one correct answer to the question. If a tool or piece of software gets it wrong that's a fault in the tool. Pressing the x button shouldn't cause an evaluation of the preceding sum, but it does.

Although I suspect (similar to the other discussion) that it's a bit of a double negative, the tool gets it wrong deliberately because people expect it to work that way because that's the way it's always worked. If it started doing it right it would confuse people.

zagfles

AmityNeon said:

zagfles said:

There are other examples. Eg

x^2 = y^2.

So logically, x = y, right? Same operation both sides?

No, because the concept of a double negative is still logical. If I owe three people a negative debt of £3 each, it equally means three people each owe me £3. I can go up uphill forwards, or turn my body around and walk backwards (whilst still moving uphill).

That's certainly logical. But I was talking about the general "logical" principle of applying the same operation to both sides of the equation.

TheBanker

Nobody has answered my question.

If showing the rate as 7% AER is deceptive, how should the bank describe the interest?

zagfles

AmityNeon said:

zagfles said:

AmityNeon said:

zagfles said:

AmityNeon said:

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.

We're probably entering the realms of extreme pedantry here which will futher annoy all those who are avidly reading this thread yet want it closed...but what you consider rules of logic I consider rules of maths. You said earlier it's "logical" that operations are performed on both sides give logical consistency. Multiplying/dividing by 0 is an operation. It's the rules of maths that says dividing both sides by the same value gives a consistent equation, except where that special mathematical concept of zero is involved.

Are you saying it's not logical for that to be the case? Is it only 'mathematically correct' because the rules of mathematics say so? Do you think such rules are derived from logic, arbitrarily, biology, the scientific method, or ethics and philosophy?

I'm not saying logic alone without education can address all manner of mathematical problems, but in terms of consumer finance, it's discouraging to others if they feel they need to be 'learned' in maths when basic arithmetic and logic are all that are necessary. People don't have to like something to be able to do it, but it's in their (and everyone's) best interests to think logically and critically, and they should feel confident they can do so in all areas of life instead of believing they're just no good at maths and switching off because they haven't learned or remembered the 'rules of maths'. I only have a GCSE in maths myself, and I'm certainly not academically gifted.

It's the opposite IMO. If people are told they should be able to solve everyday maths problems just applying inate logic, but they can't, that will discourage them. They're told they should be able to do something without being taught how and if they can't they're illogical.

If you show them rules and techniques to solve problems, then they can use them next time. It's no different to teaching children how to add up. Start at the right, add the digits, if it's over 10 carry one etc. Some people may be able to work out how to add or multiply two numbers inately, but most will use techniques and rules they were taught at school.

Same for more advanced stuff, like compound interest, mortgage repayments, algebra etc. They don't need to "remember" rules, they can look them up. But if they use them regularly the main rules will stick.

It's not a case of they 'should' be able to solve everyday maths problems with innate logic; they can do it. It's the inherent 'can-do' attitude, instead of dismissing things outright because they're confronted with lines and lines of letters, numbers and symbols. 'Good at maths' in the vernacular is more akin to Carol Vorderman or Rachel Riley quickly formulating arithmetic solutions to hit seemingly impossible targets (within 30 seconds); that is far more difficult than understanding consumer finance, which is more akin to finding five-letter words.

Do you not think children should be taught how to add up, should they just be told to work it out logically?

Personal finance can involve some complicated maths. How much will you have in 10 years if you save £100 per month at a growth rate of 4%? How much will you need in your pension pot to be able to draw £500 a month for the next 30 years assuming a growth rate of 2% above inflation? 

You could work it out from first principles using "logic", you could use a spreadsheet, or you could look up the geometric progression formula.

I love countdown, but again learning techniques is useful. I was rubbish at it at first, now I get ones Rachel fails at. But it's through learning techniques. I worked them out, but you can be taught them.

AmityNeon

Bridlington1 said:

AmityNeon said:

zagfles said:

There are other examples. Eg

x^2 = y^2.

So logically, x = y, right? Same operation both sides?

No, because the concept of a double negative is still logical. If I owe three people a negative debt of £3 each, it equally means three people each owe me £3. I go up uphill forwards, or turn around and walk backwards (still moving uphill).

But up until relatively recently the concept of negative numbers was seen as illogical. If you go back even to the early to mid 19th century it was common practice to ignore negative results derived from equations on the assumption that they were meaningless. The logic was that negative numbers can't exist physically in the real world, i.e. you can't have -3 apples, or -3 pound coins.

Numbers themselves don't exist physically in the real world; they're a conceptual frame of understanding through which we interpret the world around us. There could be three apples in a bowl to represent the concept of '3', but when I eat those three applies, it becomes:
Bowl: -1 -1 -1
Stomach: +1 +1 +1

Bridlington1 said:

What is logical is a largely subjective question since it's mostly about perception. If you don't understand a concept you will likely see it as illogical just as countless mathematicians in bygone eras saw negative numbers as illogical. At the time they couldn't understand them physically so they viewed them as illogical.

Something only really becomes logical to you if you understand it, if you don't understand it it probably won't seem all that logical.

Logic is logical; it's not always simple to grasp, especially in counterintuitive contexts, which is why critical thinking is important. It also doesn't help when established 'systems' (including religion/politics) hamper the progress of knowledge.

zagfles said:

AmityNeon said:

zagfles said:

There are other examples. Eg

x^2 = y^2.

So logically, x = y, right? Same operation both sides?

No, because the concept of a double negative is still logical. If I owe three people a negative debt of £3 each, it equally means three people each owe me £3. I can go up uphill forwards, or turn my body around and walk backwards (whilst still moving uphill).

That's certainly logical. But I was talking about the general "logical" principle of applying the same operation to both sides of the equation.

What about it? You must apply the same operation to both sides of an equation; that has no relation to forcing logic to somehow deduce that x = y.

RG2015

TheBanker said:

Nobody has answered my question.

If showing the rate as 7% AER is deceptive, how should the bank describe the interest?

I did say earlier that to show a rate of 3.69% as per the thread title would be equally as wrong, (if not even more “deceptive”).

I haven’t read the whole thread in detail, however I think the consensus is that the word deceptive is inappropriate.

What I believe is that showing the headline rate as 7% without any “headline” caveat, can lead to some people misunderstanding the expected yield.

We need a simple, concise way of making it very clear that the nature of a 12 month RS meant the yield would only be about half of a simple 7% x £3,600.”

I did say concise, so it would require the skills of a mathematical wordsmith to achieve this more successfully than is currently the case.

Cue for forum wordsmiths to enter the fray (if they ever get this far in such a varied and  “booooring” collection of posts).

eskbanker

AmityNeon said:
There could be three apples in a bowl to represent the concept of '3', but when I eat those three applies, it becomes:

Bowl: -1 -1 -1
Stomach: +1 +1 +1

It was only a matter of time before someone on this thread got to the core issue....

zagfles

TheBanker said:

Nobody has answered my question.

If showing the rate as 7% AER is deceptive, how should the bank describe the interest?

I remember a RS account that had a nominal rate of 6% but showed an AER of 6.1% or similar. Interest was paid annually at the end of the term. Apparently it was technically correct but arguable deceptive. AER is far more complicated than most people think, it can depend on expected cashflow, so a nominal annually paid rate is not necessarily the same as the AER.

AmityNeon

zagfles said:

Do you not think children should be taught how to add up, should they just be told to work it out logically?

Where did I give that impression? Just because arithmetic can be logically deduced without learning doesn't mean I advocate for not teaching children arithmetic; in fact, the teaching of basic arithmetic is conducted through logic, purely because it's logical, i.e. it simply makes sense and is easy to grasp. This is unlike other disciplines where specific facts must be remembered to form part of accumulated knowledge and wisdom.

zagfles said:

Personal finance can involve some complicated maths. How much will you have in 10 years if you save £100 per month at a growth rate of 4%? How much will you need in your pension pot to be able to draw £500 a month for the next 30 years assuming a growth rate of 2% above inflation?

You could work it out from first principles using "logic", you could use a spreadsheet, or you could look up the geometric progression formula.

Do you have a problem with logic? Logic is the basis for those first principles and a spreadsheet simply helps crunch the numbers. What I don't expect the average person to do is derive the formula themselves solely through logic, as that requires an interest in maths.

zagfles

AmityNeon said:

Bridlington1 said:

AmityNeon said:

zagfles said:

There are other examples. Eg

x^2 = y^2.

So logically, x = y, right? Same operation both sides?

No, because the concept of a double negative is still logical. If I owe three people a negative debt of £3 each, it equally means three people each owe me £3. I go up uphill forwards, or turn around and walk backwards (still moving uphill).

But up until relatively recently the concept of negative numbers was seen as illogical. If you go back even to the early to mid 19th century it was common practice to ignore negative results derived from equations on the assumption that they were meaningless. The logic was that negative numbers can't exist physically in the real world, i.e. you can't have -3 apples, or -3 pound coins.

Numbers themselves don't exist physically in the real world; they're a conceptual frame of understanding through which we interpret the world around us. There could be three apples in a bowl to represent the concept of '3', but when I eat those three applies, it becomes:
Bowl: -1 -1 -1
Stomach: +1 +1 +1

Bridlington1 said:

What is logical is a largely subjective question since it's mostly about perception. If you don't understand a concept you will likely see it as illogical just as countless mathematicians in bygone eras saw negative numbers as illogical. At the time they couldn't understand them physically so they viewed them as illogical.

Something only really becomes logical to you if you understand it, if you don't understand it it probably won't seem all that logical.

Logic is logical; it's not always simple to grasp, especially in counterintuitive contexts, which is why critical thinking is important. It also doesn't help when established 'systems' (including religion/politics) hamper the progress of knowledge.

zagfles said:

AmityNeon said:

zagfles said:

There are other examples. Eg

x^2 = y^2.

So logically, x = y, right? Same operation both sides?

No, because the concept of a double negative is still logical. If I owe three people a negative debt of £3 each, it equally means three people each owe me £3. I can go up uphill forwards, or turn my body around and walk backwards (whilst still moving uphill).

That's certainly logical. But I was talking about the general "logical" principle of applying the same operation to both sides of the equation.

What about it? You must apply the same operation to both sides of an equation; that has no relation to forcing logic to somehow deduce that x = y.

OK, using your logic, work out the amount of energy your solar panels would generate on a sunny day. I guarantee you won't be able to do it without using calculus. If you can work out how to use calculus from first principles without being taught it or looking it up, I'll be mighty impressed!