Suppose we have an inflation in a country with an annual 2% and we get a loan for an annual 1% (real interest). Is the money we receive free? This is a common practice in some European countries, where the mortgages are around 1% fix rate plus the Euro Interank Offered Rate. If so, why? Are the banks loosing money by lending in such low rates?
"Real interest" means the interest after subtracting inflation. Interest including inflation would be called "nominal interest".
If inflation is 2%, then 1% real interest means 3% nominal interest, which is the interest that is written in the loan contract and is what you actually have to pay. You would have to pay \$300 interest on a \$10000 loan. However, if you put the \$10000 into a savings account that matched inflation, you would have \$10200 at the end of it. So you would have lost \$100 overall.
Inflation: 2% Interest: 1%
This means the real rate is 3%. So no; not free money.
Free money would be negative interest rates. Example: Inflation: 0%. Interest on loan I get from the bank: -1%. This would mean they are paying ME 1% to take the loan from the bank.
Negative interest rates are a real practice, with many historical examples that can be researched.
The banks are theoretically losing 1%(+2% inflation) on the loaned amount, however it's important to understand that deals are made among negotiations with central banks in the background that can still produce gains from this.
You have the right intuition.
However, 1% is usually the real interest rate.
Real interest rate = nominal interest rate - inflation
So, you are actually, usually, paying a 3% annual rate.
If that is not the case, your question does not specify if 1% is nominal or real, then just having inflation of x% does not mean that you are increasing your wealth my that much each year.
Example: Inflation is 10%. The best investment opportunity provides a return of 0.5%. By the end of the year, I am still losing 9.5% of my wealth. But does that mean that I should not invest at all? If I don't then I will lose 10% which is wrose.
I hope that helps.