Your "Inflationary Dollar," how much is it worth today?

Imagine that on the day you were born, your parents placed a dollar bill in a magic box.  The magical properties of this box change the contents to match the changes in the Consumer Price Index.   When the CPI increases, the amount of money in the box decreases because inflation erodes its value.  Likewise when the CPI decreases, the amount in the box increases as deflation increases its value.  Given the changes in the CPI since your birth, how much money do you think you'd find in your magic box if you opened it today?

You can calculate a manual solution as follows.

The solution results from this equation.

  birth year CPI                    X

-------------------------      =      ---------

current year CPI                  $1

Solving for X tells us what the purchasing power of today's dollar would be in the year of the person's birth.  For example,  I was born in 1947.  The CPI (1982-84=100) stood at 22.3.  The CPI for 1998 is 163.  Therefore, X = 22.3/163 or .1368.  Rounded off that is 14 cents.

Reversing the equation (finding what $1 from the person's birth year would purchase today), you see

  birth year CPI                   $1

-------------------------      =      ---------

current year CPI                   X

For easier reading, we can express the equation as 

current year CPI 

-----------------------      =     X

   birth year CPI

Solving this for my birth year we find that a 1947 dollar would purchase $7.31 worth of goods (rounded off to the nearest penny) at the end of 1998. In other words, its value is 1/7.31 of what it was.   This (rounded) divides out to same 14 cents we calculated with the first equation.