# Can interest and inflation rates be combined?

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
• 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. – Doug M Jan 25 '17 at 18:02
• 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. – user247327 Jan 25 '17 at 18:03
• It does not have inflation because I'm not sure where to put it. Where would it go in the formula? – Ralph Jan 25 '17 at 18:03
• 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 $FV= PV \cdot \frac{(1+R)^{n}}{\prod_{i=1}^{n}(1+\pi_{i})}$. – kolobokish Jan 25 '17 at 18:08

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

• Thanks. That is what I was looking for. I am assuming all values stay constant (maybe not realistic :-) ). – Ralph Jan 25 '17 at 18:08
• 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. – BranchedOut Jan 25 '17 at 18:24
• That is even better. That specifically answers my question of how the two combine. – Ralph Jan 25 '17 at 18:25
• I assume that I can combine them that way in any formula that involves both (e.g. future value of money with monthly contributions). – Ralph Jan 25 '17 at 18:27
• 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 – BranchedOut Jan 25 '17 at 18:31