Risk Free Rate and Inflation

CFA Level I
#1

An investor expects to receive an interest rate r which comprises:

r = Real risk-free interest rate + Inflation premium + Default risk premium + Liquidity premium + Maturity premium

Why are Real risk-free interest rate and inflation separate? I thought the Real risk-free interest rate exists to compensate for inflation?

In the book there is a definition:

The real risk-free interest rate is the single-period interest rate for a completely risk-free security if no inflation were expected. In economic theory, the real risk-free rate reflects the time preferences of individuals for current versus future real consumption.

So the definition is an axiom which specifically states that it’s the required rate of return if no inflation was to be expected, but isn’t the whole premise of interest rates to compensate for inflation first and foremost? So if a AAA country with no default risk, no liquidity premium and no maturity premiums lent say 1B dollars, then if there is no inflation, 1B today is the same as 1B a year from now so the inflation premium should = real risk-free interest rate???

#2

Real interest rates do not include inflation; nominal interest rates include inflation.

#3

Folowing the explanation, is the Inflation rate deduted from the risk free rate?

#4

If you’re given a _ nominal _ risk-free rate, you would deduct inflation to arrive at a real risk-free rate.

You wouldn’t deduct inflation from a _ real _ risk-free rate.