Real interest rate
An interest rate, paid or received, after excluding the effects of inflation.
Thus if the expected rate of inflation is 4% and one may borrow at 6% nominal on a similar compounding basis, the real rate of interest may be taken as approximately +2% (= 6% - 4%).
If one could borrow at 3% nominal and inflation were 4% as before, the real rate would be approximately 3% - 4% = -1%.
Do not overlook the possibility of negative nominal interest rates. Central banks have been known to "pay" negative interest rates on banks' deposits with them - and some have achieved the same effect by imposing equivalent charges.
Even with a negative nominal interest rate, the real rate of interest may be positive or negative according to the nominal rate's relationship with the expected rate of inflation (that may itself be positive or negative).
Of course the use of "expected" inflation above means that, because different people will have different views on inflation, the real rate of interest is an estimate varying, perhaps significantly, according to who is making the estimate.
Decompounding calculation of real interest rate
When inflation rates and money interest rates are small, the real interest rate can be estimated fairly accurately with a simple subtraction:
For example, as above:
0.06 - 0.04 = 0.02
More strictly, because the real rate and the inflation rate compound together, they would be decompounded to calculate the real rate as follows:
(1.06 / 1.04) - 1
Similarly, where the nominal borrowing rate is 3% and the inflation rate 4%, the strictly calculated real rate is:
(1.03 / 1.04) - 1
= - 0.0096
= - 0.96% (negative)