Interpolating Credit Spread

Can anyone explain how you interpolate credit spreads? I really can’t follow this math and don’t like the weighting methodology. Looking at this problem, here is what I want to calculate:

10-year spread = 5-year spread + [(10-5) / (15-5)] * (15-year spread – 5-year spread) → why is my logic failing here?

The 10-year spread may not follow the 5-year and 15-year spreads; i.e., the 10-year bond may be seen as more risky or less risky than the 5-year and 15-year bonds.

You need to find the 10-year risk-free yield (your approach works for that: use yield instead of spread), then calculate the spread.

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Thank you!

My pleasure.