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?

\(v_1 = (1-0.2)v_0 = 0.8v_0\\ v_2 = (1+0.3)v_1 = 1.3(0.8)v_0 =1.04v_0\\ \dfrac{v_2}{v_0} = 1.04 = (1+0.04)\\ \text{Overall there was a 4% increase in the stock value}\)

Let P be the original price of the stock

So we have, after two days

[ P (.80) ] (1.30) =

P * 1.04 ⇒ i.e., the stock has increased in value by 4%