A Freddie Mac quarterly statement (May 2010) reported that U.S. home sales for one of the central regions (including Illinois, Indiana, Ohio, and Wisconsin) have shown that home values decreased by 3.4% in the last previous year. What if someone interprets this information by saying, “The decrease in home sales is of concern. The decreased rate of 3.4% amounts to a decrease of 17% over five years and 34% over ten years.”
a. Explain what is incorrect about this statement.
b. If, in fact, the current median house price for this region is $175,000 and in each of the next 10 years the house values decrease in price by 3.4% relative to the previous year, then what is the estimated house value after a decade?
What percentage decrease occurs for the decade?
a. The statement is referring to additive growth, but this is multiplicative growth. There is an exponential relation between these variables.
b. ŷ = 175,000 × 0.96610 = 123,825; the percentage decrease for the decade is about 29.2%.