Average payment increase

M

Maths in space

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Hi guys,

It has always interested me how a person who will be selected for a Mars mission will have to be an expert in Maths and coding, like for instance Matt Damon;-)

I was never really good at maths in high school and ended up in a class described — unusually — as ‘Maths in space’. I say unusually because it was the lowest unit, yet maths for space would require the highest or most advanced students. I think ‘Maths in community’ might have been more accurate, although admittedly it would not help me as I have a maths problem which I cannot solve but which will be very easy for some of you as it is an everyday calculation, and it comes to this:

In a period of 42 months a premium has gone up by $273.40.

On 13/10/2015 it was: $422.40/month.
On 16/04/2019 it was: $695.80/month.

Obviously on 14/10/2015 it didn’t shoot up by $273.40, that has been a gradual increase, so the amount is not going to be $273.40 x 42 months. But what is it?

I want to find out out how much more has been paid over that period of time in premium? Another way of asking the question is: if the increase didn’t occur, how much would I have saved if I was paying $422.40/month for that 42 month period.

Not sure if it helps, but that period equals 1,282 days.

Cheers,
Dan
 
Since months are not all really the same number of days, I'd leave everything in terms of months.

But the question can't really be answered without knowing how the premium increased over time. Did it jump up on a couple occasions, but stay (about) the same in between? Or did it increase uniformly, by the same amount each month?

Suppose you know it is the latter, a uniform rate of increase. Then what you are asking for is the sum of an arithmetic series; if you are not familiar with that, look it up, and give it a try. Then also see what you would pay if it had been the average of $422.40 and $695.80 for the entire time.

(I could say a lot more, but I suspect you will find it interesting to discover this on your own, and then we can talk about why.)
 
I cannot say that I find your description of the problem completely clear. So I may misunderstand the problem, in which case my comments may miss the mark.

My first comment is that you cannot get an exact answer without knowing exactly when and and by exactly how much the fee was raised. You are guessing that it was raised in steps, which is highly plausible but not certain. You must make further guesses on the number of steps and the amount of increase at each step. You can make reasonable guesses about the number of steps, and you can make reasonable guesses about a rule by which to calculate the amount of each increase, but guesses are not certainties, and each guess raises the possibility of new error.

My second comment is that, once you make your guesses, there are formulas that you can use, but the formulas are not obvious from basic arithmetic. You can use basic arithmetic, but it may be tedious unless you have a spreadsheet program that you know how to use.
 
Dr.Peterson said:
Since months are not all really the same number of days, I'd leave everything in terms of months.

But the question can't really be answered without knowing how the premium increased over time. Did it jump up on a couple occasions, but stay (about) the same in between? Or did it increase uniformly, by the same amount each month?

Suppose you know it is the latter, a uniform rate of increase. Then what you are asking for is the sum of an arithmetic series; if you are not familiar with that, look it up, and give it a try. Then also see what you would pay if it had been the average of $422.40 and $695.80 for the entire time.

(I could say a lot more, but I suspect you will find it interesting to discover this on your own, and then we can talk about why.)
Click to expand...

Hi Dr. Peterson,

Thank you for your reply.

To answer your questions and to address your point in parenthesis:

I don't think it matters how the premium increased over time because a good argument can be made that a uniform increase is equitable without evidence to the contrary, namely what you say about it possibly jumping up on a couple of occasions but staying the same in between. Theoretically, it may have also decreased early on before beginning its climb. However, such information is not available without a lot of "heavy-lifting" on my part, and a uniform increase is equitable to both parties if a dispute was to arise.

In relation to "arithmetic series", also known as "arithmetic progression" -- is a mathematical explanation about terms in the sum of a sequence, however it is beyond my capability as it follows a formula which I am entirely deficient in applying. To that extent, I find it interesting that it exists, but it would not interest me to test with the above numbers as the ability is just not there on my part so that I could accomplish anything beyond personal frustration.
 
JeffM said:
I cannot say that I find your description of the problem completely clear. So I may misunderstand the problem, in which case my comments may miss the mark.

My first comment is that you cannot get an exact answer without knowing exactly when and and by exactly how much the fee was raised. You are guessing that it was raised in steps, which is highly plausible but not certain. You must make further guesses on the number of steps and the amount of increase at each step. You can make reasonable guesses about the number of steps, and you can make reasonable guesses about a rule by which to calculate the amount of each increase, but guesses are not certainties, and each guess raises the possibility of new error.

My second comment is that, once you make your guesses, there are formulas that you can use, but the formulas are not obvious from basic arithmetic. You can use basic arithmetic, but it may be tedious unless you have a spreadsheet program that you know how to use.
Click to expand...

Hi JeffM,

Thanks for your narrow reply.

I think since the payments were paid in monthly instalments it is safe to say that there were 42 steps, being the span in months throughout which the increase occurred. Even though a step, at least initially, might have evidenced a decrease, a uniform monthly increase is apposite to ascribe to the problem. See: What I said in reply to Dr. Peterson.

I accept that mathematics is about precision and certainty, but for me it is far better to have a working process with a reasonable final figure than to have nothing at all, and on that I seek the forum's input, since it would be difficult for me to accomplish even with the use of a spreadsheet program.
 
Maths in space said:
Hi guys,

It has always interested me how a person who will be selected for a Mars mission will have to be an expert in Maths and coding, like for instance Matt Damon;-)

I was never really good at maths in high school and ended up in a class described — unusually — as ‘Maths in space’. I say unusually because it was the lowest unit, yet maths for space would require the highest or most advanced students. I think ‘Maths in community’ might have been more accurate, although admittedly it would not help me as I have a maths problem which I cannot solve but which will be very easy for some of you as it is an everyday calculation, and it comes to this:

In a period of 42 months a premium has gone up by $273.40.

On 13/10/2015 it was: $422.40/month.
On 16/04/2019 it was: $695.80/month.

Obviously on 14/10/2015 it didn’t shoot up by $273.40, that has been a gradual increase, so the amount is not going to be $273.40 x 42 months. But what is it?

I want to find out out how much more has been paid over that period of time in premium? Another way of asking the question is: if the increase didn’t occur, how much would I have saved if I was paying $422.40/month for that 42 month period.

Not sure if it helps, but that period equals 1,282 days.

Cheers,
Dan
Click to expand...
As I understand your problem statements and explanations:

Without "any increase", the total premium paid would have been = 422.40 * 42 = $ 17740.80

With "linear increase", the total premium paid would have been = (422.40+695.80)/2 * 42 = $ 23482.20
 
It makes a huge difference how the premium increases; but it is not unreasonable to suppose that it increased by the same amount each month, if you aren't an accountant responsible for exact amounts. I'll keep things simple.

If there was no change until after the last month, the total would be, as has been said, 422.40 * 42 = $17,740.80.

If these was an immediate change the first month, and then it stayed unchanged, the total would be 695.80 * 42 = $29,223.60.

If the change took place in 42 equal steps (an arithmetic series), then the total would be average of these two, (17,740.80 + 29,223.60)/2 = $23,482.20. That is the fact that I thought you might find interesting: you don't need to do anything fancy. I won't bother to go into why this is.

So the increase in the total is just 23,482.20 - 17,740.80 = $5,741.40. That's half of the increase that would have resulted from making the increase all at once at the start; and it's the same total increase you'd get if the increase were made all at once halfway through.
 
Dr. Peterson and Subhotosh Khan,

Thank you for your replies, which have effectively solved this problem.

Can I say that when Subhotosh provided his reply I was excited to discern that the figure to be arrived at would be $23,482.20 - $17,740.80. Subhotosh permitted me that one, what must be, an elementary problem to solve, and it is exciting to see an answer so cheers for that. Dr Peterson, on the other hand confirmed my excitement was well-placed by confirming the answer, so thank you for keeping it simple with the addition of the other possibilities, in addition.

I see that (by borrowing Subhotosh's descriptions) there were two terms -- the 'without any increase' and the 'with linear increase', and by subtracting the former from the latter we have arrived at a figure which represents an amount in savings.

This solves the problem and I would like to repay the members of the forum by providing some forum assistance for others, however not only would it not be needed what I could provide would be limited;-)

Postscript: I like the precision of your avatar Dr. Peterson, and I note your impressive reply count on this forum, Subhotosh.
 
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