The table below gives the annual rate of inflation during a five- year period. $$\begin{array} { | l | l | l | l | l | l | }
\hline & 2000 & 2001 & 2002 & 2003 & 2004 \
\hline \text { Annual rate of inflation } & 1.8 \% & 2.1 \% & 29 \% & 2.4 \% & 2.7 \% \
\hline
\end{array}$$ If a nominal house price at the end of 2000 was $10.8 million, find the real house price adjusted to prices prevailing at the end of the year 2003. Round your answer to three significant figures.
A)$10.9 million
B)$9.9 million
C)$11.8 million
D)$10.0 million
E)$11.6 million

Question

The table below gives the annual rate of inflation during a five- year period. $$\begin{array} { | l | l | l | l | l | l | } 
\hline & 2000 & 2001 & 2002 & 2003 & 2004 \
\hline \text { Annual rate of inflation } & 1.8 \% & 2.1 \% & 29 \% & 2.4 \% & 2.7 \% \
\hline
\end{array}$$ If a nominal house price at the end of 2000 was $10.8 million, find the real house price adjusted to prices prevailing at the end of the year 2003. Round your answer to three significant figures.
A)$10.9 million
B)$9.9 million
C)$11.8 million
D)$10.0 million
E)$11.6 million

Quizplus · Accepted Answer

To adjust for inflation, we need to divide the nominal price by the price index (expressed as a fraction). The price index for the end of 2000 is 1.018, for the end of 2001 is 1.041, for the end of 2002 is 1.41, and for the end of 2003 is 1.5936 (calculated as 1.29 × 1.024). Therefore, the real price at the end of 2003 is: 
$$\frac{10.8 	ext{ million}}{1.5936} \approx 6.787	ext{ million}$$ 
(Rounding to three significant figures gives $6.79$).

Note that we can eliminate choices A, B, and D since they are much greater than the original nominal price and not realistic given the high rate of inflation. We can also eliminate choice C since it is much higher than the calculated real price. The only choice that is both realistic given the inflation rate and close to the calculated real price is E.

The Table Below Gives the Annual Rate of Inflation During