### Instruction: 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?### Response: To find the overall percent increase, I need to compare the final value of the stock to the initial value.
Let me call the initial value x, and then find the final value in terms of x.
On the first day, the stock decreases by $20\%$, so it loses one-fifth of its value. That means the value at the end of the first day is four-fifths of x, or $0.8x$.
On the second day, the stock increases by $30\%$ of its value at the end of the first day, so it gains three-tenths of $0.8x$. That means the value at the end, or the final value, is $0.8x + 0.3(0.8x)$, which simplifies to $1.04x$.
So the final value is $1.04x$, which is $4\%$ more than the initial value of x.