# Thread: How to Find the Percentage of Change

1. ## How to Find the Percentage of Change

Hi,

Say I had \$1,000 in the end of the year 2007, and \$1,500 in the of 2016.

What is the function to find the annual constant change in %?

It's easy to see that the total change is 50% increase, but it's not that the annual change is 5% (50% / 10 years)..

Thanks

2. ## Re: How to Find the Percentage of Change

so you want the interest rate at which \$1000 compounded annually would get you \$1500 in 9 yrs

$1000(1+int)^9 = 1500$

$\dfrac{1000}{1500} = (1+int)^{-9}$

$\dfrac 2 3 = (1+int)^{-9}$

$\dfrac 3 2 = (1+int)^9$

$int = \left(\dfrac 3 2\right)^{1/9}-1 \approx 0.046 = 4.6 \%$

3. ## Re: How to Find the Percentage of Change

Thank you.

Please explain how did you move from step 3 to step 4?

4. ## Re: How to Find the Percentage of Change

i took the reciprocal of both sides

5. ## Re: How to Find the Percentage of Change

Great, thanks a lot

6. ## Re: How to Find the Percentage of Change

1000(1 + i)^9 = 1500
(1 + i)^9 = 1500/1000 = 1.5
1 + i = 1.5^(1/9)
i = 1.5^(1/9) - 1
i = ~.046

Standard formula:
i = (f/p)^(1/n) - 1
where:
p = present value
f = future value
n = number of periods