On January 1, 2009, the price of a certain stock was 20 percent less than its value on January 1, 2008. On January 1, 2010, the price of the stock was 25 percent less than its price on January 1, 2009. The price of the stock on January 1, 2010 is what percent of its price on January 1, 2008?

70 percent

60 percent

55 percent

50 percent

45 percent

**Solution:**

Let s = the initial price of the stock on January 1, 2008. If the value of the stock falls 20 percent, then its price on January 1, 2009 will be

$\begin{array}{l}\Rightarrow \mathrm{F}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{l}\text{Value=}\left(\mathrm{I}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}\text{Value}\right)\times \left(1-\frac{\mathrm{P}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\text{LessThan}}{100}\right)\\ \Rightarrow 2009\text{}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}=\left(\mathrm{s}\right)\times \left[\text{1-}\left(\frac{20}{100}\right)\right]\\ \Rightarrow 2009\text{}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}=\left(\mathrm{s}\right)\times \left(\frac{80}{100}\right)\\ \Rightarrow 2009\text{}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}=\frac{4}{5}\mathrm{s}\end{array}$

If the value of the stock then drops an additional 25 percent, then its price on January 1, 2010 will be

$\begin{array}{l}\Rightarrow \mathrm{F}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{l}\text{Value=}\left(\mathrm{I}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}\text{Value}\right)\times \left(1-\frac{\mathrm{P}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\text{LessThan}}{100}\right)\\ \Rightarrow 2010\text{}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}=\left(\frac{4}{5}\mathrm{s}\right)\times \left[\text{1-}\left(\frac{25}{100}\right)\right]\\ \Rightarrow 2010\text{}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}=\left(\frac{4}{5}\mathrm{s}\right)\times \left(\frac{3}{4}\right)\\ \Rightarrow 2010\text{}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}=\frac{3}{5}\mathrm{s}\\ \Rightarrow 2010\text{}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}=\left(\frac{3}{5}\text{s}\times \text{100}\right)\to \text{60\%ofs}\end{array}$

The final price of the stock is 60 percent of its original price s.

Alternatively, we could let value of the stock on January 1, 2008 be $100. Then on January 1, 2009, the price of the stock would have been $80. On January 1, 2010, the price of the stock would have been $60. Thus $\frac{60}{100}=\frac{6}{10}=60\mathrm{\%}$.