Use 82.4 as the Consumer Price Index in 1980 and 172.8 as the CPI value in 2000. If a
certain car costs $9730 in 1980, what would a similar car have cost in 2000? Show your
work.
PSOLVE
P:
The main objective of this problem is two part. First, find an inflation rate. The
next step of the problem is to apply that inflation rate to the cost of a car from 1980, and
determine the cost in 2000. A similar problem could arise in any economics situation.
According to mathworld.com, index numbers are used to compare stock in the Dow and
NASDAQ. One could easily compare stock prices from 1977 to 1990 using these
numbers. This problem will require information and formulas from chapter three in the
text book. The problem should take about ten minutes to solve.
S: The two important formulas in solving this problem are,
CPI new  CPI old
 100  I where I is the inflation rate, and
CPI old
P(1  I )  NP where I is as above, P is the original price, and NP is the new price.
The first step is to compute the inflation rate. To compute inflation one only needs to
plug the values into the formula stated above. Careful attention needs to be paid to which
value is the old, and which value is the new. In this case I am comparing 2000 to 1980 so
2000 is the new value and 1980 is the old value.
172.8  82.4
100%  110
82.4
The next step is to apply the formula for new price from above.
(110  100%)$9730  $20,433
The answer $20,433 is the price of the car in 2000.
To double check the problem one would need to work backwards to get a cost of $9730
for 1980. The backwards problem would go something like this. Use 82.4 as the
Consumer Price Index in 1980 and 172.8 as the CPI value in 2000. If a certain car costs
$20,433 in 2000, what would a similar car have cost in 1980?
82.4  172.8
 100  52%
172.8
(52%  100%)$20433  $9807
Initially I was worried because $9807 is not equal to $9730, but after some thought I
realized the differences arise because of rounding. If I take rounding into account, I can
justify my double check. Therefore, the answer makes sense.
O:
The new objects are the formulas that were explained above, and the CPI.
CPI, The CPI is an index number that is created to allow financial time periods to easily
be compared. It is tempting to leave out the second formula and just multiply the
inflation rate by the price to get the new price, but this gives the wrong answer.
L:
CPI values givenuse inflation formulause the new price formulaget a result.
V:
CPI-Consumer Price Index, A number used to compare the cost of goods in different
years.
Inflation-A measure of how the price of goods increases.
Rounding- I already knew what this word meant but it seemed to be very important in the
double check. Rounding is the act of taking a number and turning it into a more simple
number.
E:
A similar problem is: Use 82.4 as the Consumer Price Index in 1980 and 172.8 as
the CPI value in 2000. If a certain pair of shoes cost $20 in 1980, how much would that
same pair of shoes cost in 2000.
172.8  82.4
100%  110
82.4
(110  100%)$20  $42
This problem is nearly identical to the original problem. The steps to follow are the
same. The problem also uses the same formulas.
Works Cited:
Weisstein, Eric W. "Index Number." From MathWorld--A Wolfram Web Resource.
http://mathworld.wolfram.com/IndexNumber.html