[Math] Can interest and inflation rates be combined

Question

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

Answer 1

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