# Calculate exponential growth rate

Teacher's questions

### Calculate exponential growth rate

Hello

I have a problem that I couldn't find the answer to on google.

I have two known values:

Value in the year 2011 was 100
Value in the year 2016 was 112

How do I find the average annual exponential growth rate year by year? Is it possible to make this calculation in excel?
Guest

### Re: Calculate exponential growth rate

The formula is

Capital = Initial capital * (1 + np/100)

n = 5 because the period is for 5 years.
112 is the capital
110 is the initial capital
p is the percent

112 = 110 (1 + 5p/100)
112 = 110(1 + p/20)
...
Guest

### Re: Calculate exponential growth rate

I am sorry the initial capital is 100 not 110.

$112 = 100 (1 + \frac{5p}{100})$

$112 = 100 (\frac{100 + 5p}{100})$

$112 = 100 + 5p$
$12 = 5p$
$2.4 = p$
Guest

### Re: Calculate exponential growth rate

Yes but formula is wrong it must be
$$Capital = Initial capital * (1 + \frac{p}{100})^n$$

$$112 = 100 * (1 + \frac{p}{100})^5$$
Guest