I'm looking for someone to double check my math and who can tell me if I have correctly accounted for inflation.
Say you hypothetically invest $100 with 7% rate and 2% inflation. You would end up with $107 at end of one year in future dollars. In today's dollars, that is worth 107/1.02=$104.9, leading to an “effective rate” of 4.9%.
A formula I know of, which I'll call the "effective rate of return," is (1+interest rate)/(1+inflation)-1. Here it is (1+.07)/(1+.02)-1 =0.049. It correctly predicts the number above.
Some use the approximation of interest rate-inflation = .07-.02 =.05. I'm trying to interpret why it is only approximate. It is only approximate because it does not account for those 5 future dollars being worth less than $5 current dollars. (Those $5 future dollars are only worth 5/1.02=4.9 current dollars, as predicted by the “effective rate of return.")
So my question is, is the "effective rate of return" formula above the "correct" way to accommodate inflation for the purposes of calculating hypothetical future returns if one wishes to do it in today's dollars, and also if one wishes to account for inflation? I would be very thankful if someone can let me know if I had made mistakes, or if I am correct.
Edit: I think that the above formula works in all four combinations of positive/negative interest rates and positive/negative inflation rates. Above, I only presented the math for a positive interest rate with a positive inflation rate.