Expert: Paul Klarreich - 12/25/2006

Question
Paul,
can you please help me with this query; How do I calculate what $1000 in 1939 is worth in today's money? Also the reverse if possible i.e. $1000 in December 2006 value would equal in 1939 terms. Thanking you in advance and I look forward to your response. Regards

Answer
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Questioner:  Paul
Category:  Advanced Math
Subject:  Currency values over time
Question:  Paul,
can you please help me with this query; How do I calculate what $1000 in 1939 is worth in today's money? Also the reverse if possible i.e. $1000 in December 2006 value would equal in 1939 terms. Thanking you in advance and I look forward to your response. Regards
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This is a standard computation, but certain information is needed:

r = the annual percentage rate as a fraction, such as 0.05 for 5%.
f = the compounding frequency. e.b. f=4 means compounding quarterly.
y = number of years of growth.
P = original amount invested.(THEN amount)
A = amount after growth. (NOW amount)

Each compounding period multiplies the current amount by (1 + r/f).
There are  fy  of these, so:

A = P(1 + r/f)^(fy)

is your basic formula.  Obviously, y = 2006-1939 = 67 years, but you will have to determine and supply r and f.  For your questions:
................................
How do I calculate what $1000 in 1939 is worth in today's money?

Set P = 1000, find A.
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Also the reverse if possible i.e. $1000 in December 2006 value would equal in 1939 terms.

Set A = 1000, find P.  Use:
         A
P = --------------
   (1 + r/f)^(fy)

If r is not a constant, then this gets messy and the best I can say is to set it up in a spreadsheet, like Excel.
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Sorry you were not familiar with the  "^" symbol.  On this site, using the rather clumsy interface, there are lots of mathematical symbols that can't be shown well.

One of them is the 'power' symbol, and it is customary to write:

x^3

to mean  "x to the third power".  The actual "^" character is sometimes called the 'hat' or the 'circumflex' or perhaps other things, depending on the contex.  Its use here comes from the very early days of BASIC programming where a programmer would write:

LET  X = Y^3

or something like that, to indicate a power, just as it was customary to write '*' for multiplication.