Formula for working out annual compound % change

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sysiphean

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What formula would be used to calculate percentage change per annum (compounding increase)?

If a product cost $100 in 2010 and we know it now costs $300 in 2020, what formula would calculate what compounding percentage to be applied annually? I am wanting to apply a % on top of the 2010 cost for each successive year to know what the cost would be, for example, in 2006 or 2008 or 2030 etc.

I will greatly greatly appreciate some help with this one! Many thanks to any kind soul that can help me.
 
How would you do a single year?

2010 - 100
2011 - 105

What say you?
 
[MATH]\left (\dfrac{300}{100} \right )^{1/10} - 1 \approx 11.61\% \text { increase p. a.}[/MATH]
That is the average annual rate of increase. (Geometric mean.)

Stick it in excel and test it.
 
sysiphean said:
What formula would be used to calculate percentage change per annum (compounding increase)?

If a product cost $100 in 2010 and we know it now costs $300 in 2020, what formula would calculate what compounding percentage to be applied annually? I am wanting to apply a % on top of the 2010 cost for each successive year to know what the cost would be, for example, in 2006 or 2008 or 2030 etc.

I will greatly greatly appreciate some help with this one! Many thanks to any kind soul that can help me.
Click to expand...
Do you know the formula (equation) to calculate future value of an amount accruing compound interest?
 
I fear I am not explaining myself very clearly. May I say thank you for helping me, it is very good of you.

I would like to be able to apply a % figure onto of the recorded figure from one year, and apply it to each year after that. For example (if I knew how to work out the % figure to apply, which for this example I will use 12% to demonstrate):

2010 Year - Cost = $100
∴
$100 x 1.12 = $112 for the cost in 2011.
$112 x 1.12 = $125.44 for cost in 2012.
$125.44 x 1.12 = $140.49 for cost in 2013.
140.49 x 1.12 = $157.35 for cost on 2014.
END EXAMPLE

I have a start point, being the cost in 2010, and I have and end point, being the cost in 2020. I do not know how to work out the percentage figure to apply.
 
sysiphean said:
I do not Subhotosh. Would you kindly educate me? Thank you.
Click to expand...
Go to google.com and type in search word "compound interest".

I found there were ~300 million websites, with papers, videos, etc. - ready to help me.

Please peruse some of those - in your favorite mode of learning - and tell us if you are still stuck.
 
Subhotosh Khan said:
Go to google.com and type in search word "compound interest".

I found there were ~300 million websites, with papers, videos, etc. - ready to help me.

Please peruse some of those - in your favorite mode of learning - and tell us if you are still stuck.
Click to expand...
Thank you Subhotosh,

I have researched this but to no avail. I have read lots about formulas when you already know the interest rate, but not how to work out what it was between two know figures over time.

If I am an annoyance to anybody I apologise. I would be happy to pay someone for the formula if that is an option? I just lack the skills/understanding to work this out.
 
sysiphean said:
Thank you Subhotosh,

I have researched this but to no avail. I have read lots about formulas when you already know the interest rate, but not how to work out what it was between two know figures over time.

If I am an annoyance to anybody I apologise. I would be happy to pay someone for the formula if that is an option? I just lack the skills/understanding to work this out.
Click to expand...
So what is the "formula" for calculating the "compounded" future value - when you know the interest rate?
 
Subhotosh Khan said:
So what is the "formula" for calculating the "compounded" future value - when you know the interest rate?
Click to expand...
You LEGEND Subhotosh!!! Thank you!
I think I have it..... I hope I do!!!

FV = PV (1+r)n
  • FV = Future Value,
  • PV = Present Value,
  • r = Interest Rate (as a decimal value), and
  • n = Number of Periods
Therefore the below should be whatI'm after.

r = ( FV / PV )1/n - 1

So now I just need to understand how to apply that to an excel formula I think?
 
sysiphean said:
I fear I am not explaining myself very clearly. May I say thank you for helping me, it is very good of you.

I would like to be able to apply a % figure onto of the recorded figure from one year, and apply it to each year after that. For example (if I knew how to work out the % figure to apply, which for this example I will use 12% to demonstrate):

2010 Year - Cost = $100
∴
$100 x 1.12 = $112 for the cost in 2011.
$112 x 1.12 = $125.44 for cost in 2012.
$125.44 x 1.12 = $140.49 for cost in 2013.
140.49 x 1.12 = $157.35 for cost on 2014.
END EXAMPLE

I have a start point, being the cost in 2010, and I have and end point, being the cost in 2020. I do not know how to work out the percentage figure to apply.
Click to expand...
logarithms might help.

What you have shown is [math]100\cdot\left(1.12\right)^{4} = 157.35[/math]Your task is to solve: [math]100\cdot\left(1+i\right)^{4} = 157.35[/math]
Do you see how to do that?
 
Look at post 3. I already told you how to do it. A hand calculator is all you need.
 
sysiphean said:
You LEGEND Subhotosh!!! Thank you!
I think I have it..... I hope I do!!!

FV = PV (1+r)n
  • FV = Future Value,
  • PV = Present Value,
  • r = Interest Rate (as a decimal value), and
  • n = Number of Periods
Therefore the below should be whatI'm after.

r = ( FV / PV )1/n - 1

So now I just need to understand how to apply that to an excel formula I think?
Click to expand...
The equation should be written as:

r = (FV/PV)^(1/n) -1

Excel can easily solve the equation above. It may even have a standard function.

Good work!
 
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