Confusion on default-free rates

CFA Level II Portfolio Management
#1

Dear Gurus,

I have this example from CB from CFA institute.
image

What I am confused about is that, is there any difference between A (default-free nominal bond) and C (default-free inflation-indexed bonds)?

Regarding BEI, CB says difference between default-free zero-coupon bond nominal rate and real rate.
What Schweser says about BEI is that difference between yield on non-inflation indexed bond - yield on inflation indexed bond.

So I reorganized them, risk free nominal rate = risk free inflation indexed bonds, risk free real rate = risk free non-inflation indexed bonds. but having this example, it made me confused.

Another question, if you know. I am on a reading #46, The yield curve and the business cycle. It studies about correlation between yield and real economy. After they talk about economies and financial crisis suddenly talk about “Business cycle” I thought business cycle is something like “growth ->maturity” this cycle or “supply-demand, production related” cycles. Here what they mean about business cycle is about real economic activities. right? Economically good times and bad times.

Thanks teachers in advance for your help!

#2

Here is the answer for the example.
image

#3

The coupon rate on the nominal bond includes an inflation premium, while the coupon rate on the inflation-indexed bond does not. Therefore, the coupon rate on the inflation-indexed bond is a real rate while the coupon rate on the nominal bond is not.

#4

Well noted! Thanks,
What you are saying is 100% correct right?
There are a lot of explanations from different sources saying different things.