A stock investment went up $25\%$ in 2006. Starting at this increased value, what percent would it have to go down in 2007 to be back to its original price at the beginning of 2006?

20%

Step-by-step explanation:

Let x represent the initial value of the stock at the beginning of 2006. And y the value at the end of 2006.

When it went up by 25% in 2006;

y = x + 25% of x = x + 0.25x = 1.25x

For the value to go back to the original price, it has to decrease from y to x;

y = 1.25x

The percentage decrease from y to x is;

= (y-x)/y × 100%

Substituting the values;

= (1.25x -x)/1.25x × 100%

= 0.25x/1.25x × 100%

= 0.2 × 100%

= 20%

Therefore, it will have to go down 20%

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step-by-step explanation: