Final answer:
To calculate the price of the home at the end of 2012, you need to calculate the cumulative increase in house prices from 2010 to 2012. The cumulative increase is the product of the individual percentage increases.
Step-by-step explanation:
To find the price of the home at the end of 2012, we need to calculate the cumulative increase in house prices from 2010 to 2012. The cumulative increase is the product of the individual percentage increases. First, we calculate the price of the home at the end of 2010 by multiplying the initial price by 1 + the percentage increase in 2010 (1 + 0.027). Next, we calculate the price at the end of 2011 by multiplying the price at the end of 2010 by 1 + the percentage increase in 2011 (1 + 0.036). Finally, we calculate the price at the end of 2012 by multiplying the price at the end of 2011 by 1 + the percentage increase in 2012 (1 + 0.050).
So, the calculations would be:
Price at the end of 2010 = $126,400 * (1 + 0.027) = $129,802.80
Price at the end of 2011 = $129,802.80 * (1 + 0.036) = $134,358.18
Price at the end of 2012 = $134,358.18 * (1 + 0.050) = $141,076.09
Therefore, you would pay $141,076.09 for a home at the end of 2012 that listed for $126,400 at the beginning of 2010.