find average annual percentage increase, given yearly values

find the percentage increase for each year individually ...

94 to 95 = ?

95 to 96 = ?

96 to 97 = ?

97 to 98 = ?

now find the average of the 4 percentage increases in production ... you should get an average increase in scooter production of about 29.4%
 
skeeter said:
find the percentage increase for each year individually ...

now find the average of the 4 percentage increases in production ... you should get an average increase in scooter production of about 29.4%
Click to expand...

i like your answer.

but the answer given in the book is 35%
 
35% is impossible, given the data; Sir Skeeter is correct with ~29.4.

Using the data as $20 accumulating to $55 over 4 years should give
a slightly lesser rate (due to compounding); let's see:
20(1 + i)^4 = 55
(1 + i)^4 = 55/20 = 11/4
1 + i = (11/4)^(1/4)
1 + i = ~1.2877
i = ~.2877 or ~28.77%
 
defeated_soldier said:
here is the full question and the solution from the book....
Click to expand...
Ah; providing the definitions and formulas you've been given to use is generally helpful. (This is why the "Read Before Posting!!" thread asked you to include this sort of information.)

. . . . .Given a period T, the average percentage change over that period is given by:

. . . . .[percentage change over T] / [number of years (or entries) in T]

The book shows, in its solution, exactly how it arrived at its value: Find the absolute change (55 - 20), divide by the original value (20) to find the percent change over the original (175%), find the length of the period (1998 - 1994 + 1 = 5 years, inclusive), and divide the percentage by the period length.

Where are you stuck?

Eliz.
 
stapel said:
The book shows, in its solution, exactly how it arrived at its value: Find the absolute change (55 - 20), divide by the original value (20) to find the percent change over the original (175%), find the length of the period (1998 - 1994 + 1 = 5 years, inclusive), and divide the percentage by the period length.
Click to expand...
i dont want to use the formula . i want to use the basic law of mathematics first , in either way i should get the SAME answer ....is not it ?

just look at the question , i was asked to calculate average percentage change . i will use the usual method to find it out . and then i wanted to tally the result with applying the formula .

using the usual way i am getting 29.4 .

usual the formula i get 35

both are not matching and so i am stuck ....that formula is for quick calculation and i am not restricted to use the formula .

They are saying if a problem comes like that then you could use the formula and get the result very early without doing BIG BIG averages and percentages .

Hope , now you understand my concern.
 
defeated_soldier said:
i dont want to use the formula .
Click to expand...
If you don't want to use the formula that defines what they're asking for, that's fine. But you'll probably continue to end up with a different answer, since you're not doing what they asked for.

Eliz.
 
stapel said:
defeated_soldier said:
i dont want to use the formula .
Click to expand...
If you don't want to use the formula that defines what they're asking for, that's fine. But you'll probably continue to end up with a different answer, since you're not doing what they asked for.

Eliz.
Click to expand...

oh come on ....thats a shortcut tips ...i told you ......thats not a direction of a question.

you are right .....there are some questions where there are some directions are given and then some questions might be asked . you have to follow the direction to answer the questions.

For example , a direction is given
+ = multiplication
- = division

Now , this is called a direction . if this kind of direction is given and then if you are asked to solve some questions based upon this direction , then you have to obey it .



BUT , as far as my question is concerned , the rule they have given is a SHORTCUT TIPS to bypass big calculations ......this is not a direction . I am free to use their formula or go by my own way .....if i do in my own way i would get the same answer but it might take some time ....thats the only difference.

Hope , i have been able to explain you properly.

Now, ok...as far as this question is concerned , either the SHROTCUT TIPS given in the book is wrong or OUR calculation is wrong as both the answers are not matching .

However , I have full faith in the forum members , and so i conclude that the SHORTCUT TIPS is wrong and i should not use that any longer better the use the normal procedure shown by skitter and denis.

Thank you
 
defeated_soldier said:
BUT , as far as my question is concerned , the rule they have given is a SHORTCUT TIPS to bypass big calculations ......this is not a direction .
Click to expand...

NO Mathsoldier, it is NOT a shortcut tip: it is the rule that THEY DECIDED
to use to examine average annual performances.

The standard rule is:
Average Annual Percent Change is the average annual percent change over a period of several years that is calculated by taking the nth root [where n is the number of years in the period of interest] of the result of the current year’s value divided by the value of the first year of the period; this result then has 1 (one) subtracted from it and that result is then multiplied by 100.

Now it is quite possible that a company is interested in looking at annual results
in a different way from the standard rule; they make up a rule to suit themselves,
and UNFORTUNATELY still call it "Average Annual Percent Change"; usually, the
purpose is to make themselves look better!
 
defeated_soldier said:
...the rule they have given is a SHORTCUT TIPS to bypass big calculations.
Click to expand...
No; the rule (formula) they gave IS the calculation. There is nothing else.

You can do something else if you like, you can create a different definition for their term if you like, you can invent a different formula ("direction") if you like. But that doesn't change the fact that they told you to use something else.

Using your own method ("direction") is going to produce your own result. There is no "error" in their computations. The only error is in assuming that you can make up a new method and still get the old result.

It is to be regretted if that offends or upsets you, but I'm afraid those are the facts. Sorry.

Eliz.
 
Denis said:
NO Mathsoldier, it is NOT a shortcut tip: it is the rule that THEY DECIDED to use to examine average annual performances.

The standard rule is...
Click to expand...
Ok .

Average Annual Percent Change is the defintion then whatever is given in book.

fine.

but whatever , we have calculated in this forum (by skitter) what is that called then ? does it call some thing else ?something like "Average percent chnage BUT not annula " ? or what is it ?
 
For someone "defeated", you sure do a lot of fighting :wink:

What Skitter aka Skeeter gave you was simply another way to do
the calculation; could be he'll take a Patent on it :idea:
 
defeated_soldier said:
...whatever , we have calculated in this forum (by skitter) what is that called then ?
Click to expand...
It was the tutor's best guess as to what the book meant, because you had not provided the definition we were supposed to use. Please read the earlier replies, wherein this was explained to you.

The "standard" rule for the given term is the one explained by the tutor you quoted. So please read that reply to obtain the answer you seek.

Thank you.

Eliz.

P.S. If I may venture to suggest, this tutoring process would likely be much less painful if you could please start providing the entire text of and instructions for exercises (so we aren't left guessing at what the book meant), and please use standard English formatting (so we don't have to attempt decipherment of what you meant) to clearly show all your reasoning (so we don't have to imagine what your intermediate steps were).

Then please take the time to thoroughly read the complete texts of the replies provided (so we won't need to repeat ourselves and re-explain each other's replies to you).

By using this method, perhaps we can avoid upsetting / offending you quite so frequently.

Thank you for your consideration.
 
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