A stock is expected to pay a dividend of $0.5 at the end of the year (D1=0.5), and it should continue to grow at a constant rate of 7% a year. If its required return is 12%, what is the stock's expected price 5 years from today?

You can Derive the answer like this. Using simple dendritic growth model.

$0.5 / (12% - 7%) = $10

Now to get the expected price 5 years from today, do this: $10 x (1 + 7%) ^5 = $14.03

What we did was we used the annual growth rate and calculates the growth over the next 5 years.

The stock's expected price 5 years from today is $14.03

Explanation:

Today's stock price: $0.5 / (12% - 7%) = $10

Because the stock should continue to grow at a constant rate of 7% a year, the stock's expected price 5 years from today: $10 x (1 + 7%) ^5 = $14.03