Total Percent increase If the price of an item is increase by 8% from 2005 to 2006. then from 2006 to 2007 it is also increased by 8%. what is the total percent increase in price of an item from 2005 to 2007.?
 A: HINT: $8$% of a number $p$ is $0.08p$, so when you increase $p$ by $8$%, you get $p+0.08p$. Factor out the $p$ to write this as $$p+0.08p=(1+0.08)p=1.08p$$ to see that increasing $p$ by $8$% is the same as multiplying $p$ by $1.08$. If you do it again, you multiply by $1.08$ again, getting $1.08^2p$, or $1.1664p$. This increases $p$ by what percentage?
A: Let the initial price be 100.
Then by increasing the price by 8% the New price at the end of 2006 becomes:
$$100*\left(1+{8\over100}\right)$$
Now if you increase the price again by 8% the New price at the end of 2007 becomes:
$$100*\left(1+{8\over100}\right)*\left(1+{8\over100}\right) $$
Which simplifies to: 
$$100*\left(1+{16.64\over100}\right)$$
Hence the Cumulative % increase from 2005-2007 is 16.64%
A: A "percentage increase" $p$ implies that you are adding that percentage to the total $t$, like so:
$$t+pt$$
If you apply a second increase, you must reference the new total:
$$(t+pt)+p(t+pt)=t(1+p)(1+p)=t(1+p)^2$$
Here, $p$ is taken as the real-number representation of the percentage, i.e., $p=0.08$.  The final result is as follows:
$$t(1.08)^2=t\cdot 1.1664$$
The percentage increase is calculated by subtracting the original total $t$ and dividing by that value:
$${t\cdot 1.1664 -t\over t}=1.1664-1=0.1664$$
Returning to units of "percent" we see that this is a $16.64$% increase over the two-year period.
