7.0% actually 3.69%?

AmityNeon

RG2015 said:

AmityNeon said:

RG2015 said:
And with respect, whilst I appreciate that you have posted a long explanation, I have no interest in reading it let alone attempting to critique it.

Just so we're clear, you asked for an explanation which I provided; you chose not to read it.

You did choose to read a one-sentence summary and chose to critique that instead, saying it was unclear.

The  only thing that I found unclear was the one-sentence summary. You have now clarified that.

Everything else is irrelevant.

It wouldn't have been unclear had you chosen to read the explanations you originally asked for.

EthicsGradient

Perhaps it's worth pointing out that @AmityNeon was demonstrating a different calculation they had once performed (whether it was worth stopping one regular saver, and starting a different one, with the money so far stored in an easy access account) that no one else had been talking about. I think the idea was just to show that you can use algebra to look at various calculation. It's not that surprising that few want to look at this specialised calculation (not, for instance, applicable to First Direct, since you lose interest if you pull out of that mid-way).

RG2015

AmityNeon said:

RG2015 said:

AmityNeon said:

RG2015 said:
And with respect, whilst I appreciate that you have posted a long explanation, I have no interest in reading it let alone attempting to critique it.

Just so we're clear, you asked for an explanation which I provided; you chose not to read it.

You did choose to read a one-sentence summary and chose to critique that instead, saying it was unclear.

The  only thing that I found unclear was the one-sentence summary. You have now clarified that.

Everything else is irrelevant.

It wouldn't have been unclear had you chosen to read the explanations you originally asked for.

But you only provided the explanations after I had requested clarification of one sentence that I found unclear.

AmityNeon

RG2015 said:

AmityNeon said:

RG2015 said:

AmityNeon said:

RG2015 said:
And with respect, whilst I appreciate that you have posted a long explanation, I have no interest in reading it let alone attempting to critique it.

Just so we're clear, you asked for an explanation which I provided; you chose not to read it.

You did choose to read a one-sentence summary and chose to critique that instead, saying it was unclear.

The  only thing that I found unclear was the one-sentence summary. You have now clarified that.

Everything else is irrelevant.

It wouldn't have been unclear had you chosen to read the explanations you originally asked for.

But you only provided the explanations after I had requested clarification of one sentence that I found unclear.

No. The explanation to your initial question was provided. You chose not to read it, which lead to you requesting clarification of my one-sentence summary of that explanation. Which post of mine after your request clarified my one-sentence summary, which I posted after "the explanation"?

RG2015

AmityNeon said:

RG2015 said:

AmityNeon said:

RG2015 said:

AmityNeon said:

RG2015 said:
And with respect, whilst I appreciate that you have posted a long explanation, I have no interest in reading it let alone attempting to critique it.

Just so we're clear, you asked for an explanation which I provided; you chose not to read it.

You did choose to read a one-sentence summary and chose to critique that instead, saying it was unclear.

The  only thing that I found unclear was the one-sentence summary. You have now clarified that.

Everything else is irrelevant.

It wouldn't have been unclear had you chosen to read the explanations you originally asked for.

But you only provided the explanations after I had requested clarification of one sentence that I found unclear.

No. The explanation to your initial question was provided. You chose not to read it, which lead to you requesting clarification of my one-sentence summary of that explanation. Which post of mine after your request clarified my one-sentence summary, which I posted after "the explanation"?

You are absolutely correct. But you will recall that I initially asked for a simple explanation.  What I got in response was a load of gobbledegook (to me anyway).

This resulted in a request for clarification.

I am sorry, but even if I read any of your detailed mathematical explanations I would not understand them. My brain is now addled. I am losing the will to live. I am now a broken man.

You win. You are far cleverer than me. 

AmityNeon

RG2015 said:

AmityNeon said:

RG2015 said:

AmityNeon said:

RG2015 said:

AmityNeon said:

RG2015 said:
And with respect, whilst I appreciate that you have posted a long explanation, I have no interest in reading it let alone attempting to critique it.

Just so we're clear, you asked for an explanation which I provided; you chose not to read it.

You did choose to read a one-sentence summary and chose to critique that instead, saying it was unclear.

The  only thing that I found unclear was the one-sentence summary. You have now clarified that.

Everything else is irrelevant.

It wouldn't have been unclear had you chosen to read the explanations you originally asked for.

But you only provided the explanations after I had requested clarification of one sentence that I found unclear.

No. The explanation to your initial question was provided. You chose not to read it, which lead to you requesting clarification of my one-sentence summary of that explanation. Which post of mine after your request clarified my one-sentence summary, which I posted after "the explanation"?

You are absolutely correct. But you will recall that I initially asked for a simple explanation.  What I got in response was a load of gobbledegook (to me anyway).

This resulted in a request for clarification.

I am sorry, but even if I read any of your detailed mathematical explanations I would not understand them. My brain is now addled. I am losing the will to live. I am now a broken man.

You win. You are far cleverer than me. 

It's not about winning or being clever. Which post of mine finally clarified things for you? Where did you ask for a 'simple' explanation?

Eco_Miser

AmityNeon said:

zagfles said:

AmityNeon said:

zagfles said:

AmityNeon said:

zagfles said:
You seem to be saying people don't need teaching maths or be shown mathematical techniques because they should be able to work it all out themselves.

Really? Where did I say that?

"It's not a case of they 'should' be able to solve everyday maths problems with innate logic; they can do it. "

Can do it (not 'should'); the context being adults are already educated in basic arithmetic and algebra due to compulsory maths education.

So not "innate logic", but what you've been taught! You seem to agree with me now!

(PS my last final word on this issue otherwise we'll end up going round in circles and some people may find it booooring )

Surely you understand how logic is integral to the foundation and application of maths? The ‘rules of math’ were not derived arbitrarily; it’s a formal system where logic is used to develop these ‘techniques’. One has to apply their learned knowledge with logic to solve new problems. It’s the difference between blindly following instructions using a calculator/spreadsheet and not understanding the result, and being able to decide for yourself which functions to use and why they’re appropriate for the task at hand. These decisions are all made with logic.

We also did use spreadsheets to visualise interest being accrued at discrete intervals with specific examples and daily interest, but it was useful having a generic formula that everyone could use (in the absence of a calculator).

You keep talking about 'logic'. Which logic? Aristotelian? Boolean? Something else?

You are aware that there's a flaw in the logical basis of mathematics?

Is the set of all sets that are not members of themselves a member of itself?

If it is, it isn't. If it isn't it is.

OceanSound

AmityNeon said:

RG2015 said:

I was actually intrigued how @AmityNeon derived it (or any other pertinent formula) from the GCSE maths syllabus.

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

We're familiar with m * r * 6.5, which is based on consecutively adding incremental monthly interest contributions (up to month 12). It represents the last part (right side) of the formula, of which the left side needs to be greater than the right, in order for closing/renewing our RS to be considered worthwhile.

For the left side, we need a similar formula but for a variable number of months, n.

• 1 month + 2 months + 3 months + 4 months + 5 months...
• = 1 + 2 + 3 + 4 + 5...
• = 1, 3, 6, 10, 15...

The formula for finding the value for the nth month is n(n + 1) / 2. You can visualise this intuitively like a triangle being doubled to a rectangle:

n o o o o o
n n o o o o
n n n o o o
n n n n o o
n n n n n o

In the fifth month, there are five rows of n, and inversely there are also five rows of o, but it's a rectangle as there are n + 1 columns. So however many months we've held our RS for, the formula n(n + 1) / 2 calculates how many monthly contributions of interest we've accrued. At 12 months: 12 * 13 / 2 = 78.

We know interest is calculated daily, but we approximate using monthly interest, so the annual interest rate is divided by 12. 78 monthly contributions earning 1/12 of the annual interest rate = m * (r / 12) * 78 = m * r * 6.5.

The two formulas are then merged. Instead of calculating 78, we leave the formula for n as it is, because the number of months we've held our RS for is variable (and less than 12 for this purpose).

m * (r / 12) * n(n + 1) / 2

mrn(n + 1) / 24

Dividing by 2 and then dividing by 12 is the same as dividing by 24.

So that's the first part of the left side figured out; it calculates the amount of interest accrued in our current RS. Then we close/renew...

When we restart our RS, we calculate its length up to the end of month 12 of the old RS. So if we closed our old RS at 5 months, we need to calculate the amount of interest accrued in the new RS for 7 months. This ensures that the total amount of monthly contributions earning interest on both sides of the formula is equal to 78 over 12 months (for a fair mathematical comparison).

n
n n
n n n
n n n n
n n n n n

e e e e e   S
e e e e e   S S
e e e e e   S S S
e e e e e   S S S S
e e e e e   S S S S S
e e e e e   S S S S S S
e e e e e   S S S S S S S

We can see that the 78 monthly contributions consist of three parts:

• The original 5 months, represented by the upper n triangle.
• The next 7 months, represented by the lower-right S triangle.
• The 'excess' 5 months of contributions moved into an easy-access saver, represented by the e rectangle.

We already know the formula to calculate interest over a variable number of months: mrn(n+1)/24

What's different about the S triangle? It has an increased rate of interest, so we use r + x, where x is the increase over r. The number of months is also 12 - n. We plug those values in to achieve the middle part of the left side:

m(r + x)(12 - n)(12 - n + 1) / 24

Calculating the interest for the e rectangle means we do not divide by 24, but by 12. We can visually see the dimensions of the rectangle: n * (12 - n). The reduced rate of interest is expressed as r - y. This achieves the last part of the left side and completes the formula:

m(r - y)n(12 - n) / 12

Part 1            Part 2                        Part 3
mrn(n+1)/24   +   m(r+x)(12-n)(12-n+1)/24   +   m(r-y)n(12-n)/12   >   mr6.5

The full formula can be entered into a spreadsheet for easy calculation.

It can be simplified if desired to the variants below, but that requires a stronger grasp of expanding, factoring and rearranging.

m * ((n − 12) * ((n − 13) * x + (2 * n * y)) + (156 * r)) / 24 > mr6.5

We can eliminate m and r as they're both constant on both sides of the comparison (although we lose actual interest figures as a result):

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

Please explain this bit:

"..the formula n(n + 1) / 2 calculates how many monthly contributions of interest we've accrued. At 12 months: 12 * 13 / 2 = 78..."

At 12 months we've accrued 78 monthly contributions of interest? I can't get my head round this.

OceanSound

Eco_Miser said:

AmityNeon said:

zagfles said:

AmityNeon said:

zagfles said:

AmityNeon said:

zagfles said:
You seem to be saying people don't need teaching maths or be shown mathematical techniques because they should be able to work it all out themselves.

Really? Where did I say that?

"It's not a case of they 'should' be able to solve everyday maths problems with innate logic; they can do it. "

Can do it (not 'should'); the context being adults are already educated in basic arithmetic and algebra due to compulsory maths education.

So not "innate logic", but what you've been taught! You seem to agree with me now!

(PS my last final word on this issue otherwise we'll end up going round in circles and some people may find it booooring )

Surely you understand how logic is integral to the foundation and application of maths? The ‘rules of math’ were not derived arbitrarily; it’s a formal system where logic is used to develop these ‘techniques’. One has to apply their learned knowledge with logic to solve new problems. It’s the difference between blindly following instructions using a calculator/spreadsheet and not understanding the result, and being able to decide for yourself which functions to use and why they’re appropriate for the task at hand. These decisions are all made with logic.

We also did use spreadsheets to visualise interest being accrued at discrete intervals with specific examples and daily interest, but it was useful having a generic formula that everyone could use (in the absence of a calculator).

You keep talking about 'logic'. Which logic? Aristotelian? Boolean? Something else?

You are aware that there's a flaw in the logical basis of mathematics?

Is the set of all sets that are not members of themselves a member of itself?

If it is, it isn't. If it isn't it is.

Definitely not boolean. That's to do with 1's and 0's. digital equipment like computers work according to boolean logic. 

Anyone who studies/studied electronics can confirm.

Wasn't Russell's paradox solved by Zermelo, Franekel, and Skolem (ZFC)?

Bridlington1

RG2015 said:

AmityNeon said:

RG2015 said:

AmityNeon said:

RG2015 said:

AmityNeon said:

RG2015 said:
And with respect, whilst I appreciate that you have posted a long explanation, I have no interest in reading it let alone attempting to critique it.

Just so we're clear, you asked for an explanation which I provided; you chose not to read it.

You did choose to read a one-sentence summary and chose to critique that instead, saying it was unclear.

The  only thing that I found unclear was the one-sentence summary. You have now clarified that.

Everything else is irrelevant.

It wouldn't have been unclear had you chosen to read the explanations you originally asked for.

But you only provided the explanations after I had requested clarification of one sentence that I found unclear.

No. The explanation to your initial question was provided. You chose not to read it, which lead to you requesting clarification of my one-sentence summary of that explanation. Which post of mine after your request clarified my one-sentence summary, which I posted after "the explanation"?

You are absolutely correct. But you will recall that I initially asked for a simple explanation.  What I got in response was a load of gobbledegook (to me anyway).

This resulted in a request for clarification.

I am sorry, but even if I read any of your detailed mathematical explanations I would not understand them. My brain is now addled. I am losing the will to live. I am now a broken man.

You win. You are far cleverer than me. 

Though @RG2015, you have just demonstrated there one of the greatest signs of intelligence, you know what you do not know.

The way I see it we all have areas of expertise and different ways of understanding and interpreting information. If you were to say that the position of an object can be found using the formula r = x^8, I could tell you what its snap, crackle and pop of that object is quite easily (yes these were named after rice krispies). If you throw me a question about who plays for a specific football team I wouldn't have a clue but there will likely be many forumites for whom the opposite is true.