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I am trying to understand the concept of spot rates better.

Does a 2-year spot rate indicate the rate you get for a two year bond or the rate you should discount the second year cash flow for an annual coupon bond? Same for a 3-year spot rate.

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The 2-year spot rate is the rate at which you discount the year 2 cashflows. If the bond has no coupon, has a two year maturity, and is fairly priced then the 2-year spot rate is the yield to maturity of the bond (or as you say 'the rate you get').

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