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In problems calculating the future value of money with both an interest rate and an inflation rate, how can the two rates be combined?

$$FV = PV \cdot (1 + r)^N$$

where

  • $FV$ is the future value
  • $PV$ is the present value
  • $r$ is the interest rate (combined with inflation?)
  • $N$ is the number of periods
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    It is pretty common to say that the nominal rate of interest = real rate of interest + inflation. Another approach would be to discount the adjust the Future Value into "Constant Dollars" using essentially the exact same formula. – 2017-01-25
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    The formula you give does not have "inflation" in it at all. What, exactly, is your question? Are you asking, "If you have an investment that has a future value given by this formula **and** there is inflation of rate r, what is the future value in terms of **todays** value?" If so, first use that formula to get the "value" then discount the inflation: If inflation rate is r (compounded annually), present value X, then the value in n years will be $X(1+ r)^n$. Set that equal to the furure value and solve for X. – 2017-01-25
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    It does not have inflation because I'm not sure where to put it. Where would it go in the formula? – 2017-01-25
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    Mostly there is done some procedure like this $r:=R-\pi$ (and rewrite the formula with small r). But this is approximation. The real thing is like this $FV = PV \cdot \frac{(1+R)^n}{(1+\pi)^{n}}$, or if the rate of inflation differs through years, it would be better to write $FV= PV \cdot \frac{(1+R)^{n}}{\prod_{i=1}^{n}(1+\pi_{i})}$. – 2017-01-25

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If the inflation rate, $I$, is constant then you can model the future value in equivalent present day (real) dollars, $E$, as $$E=FV/(1+I)^N=PV\cdot\left(\frac{1+R}{1+I}\right)^N.$$

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    Thanks. That is what I was looking for. I am assuming all values stay constant (maybe not realistic :-) ). – 2017-01-25
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    No problem. If you specifically wanted to replace the R with something that gave the same E, you could use R'=(R-I)/(1+I), then the above simplifies to E=PV(1+R')^N. – 2017-01-25
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    That is even better. That specifically answers my question of how the two combine. – 2017-01-25
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    I assume that I can combine them that way in any formula that involves both (e.g. future value of money with monthly contributions). – 2017-01-25
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    If you mean you can get the value in real dollars by dividing the future value by (1+I)^N, then yes I think that's right – 2017-01-25