Bill buys a stock that decreases by $20\%$ on the first day, and then  on the second day the stock increases by $30\%$ of its value at the end of the first day. What was the overall percent increase in Bill's stock over the two days?
So if the stock decreases by 20 percent, then it's only worth 80 percent of what it was before. Right, so if we call the price of the stock $x$, then after the first day it's worth $0.8x$. And then on the second day, the price increases by 30 percent of what it was at the end of the first day. So the price at the end of the second day is $0.8x + 0.3(0.8x)$. So the overall increase in price is $0.8x + 0.3(0.8x) - x$. And that expression simplifies to $0.8x + 0.24x - x$. So $1.04x - x$ is equal to $0.04x$, and $0.04x$ is equal to $4\%$ of $x$. So the overall increase in price is $4\%$. Right. So the overall percent increase in Bill's stock over the two days is $4\%$.

