Linear Interpolation – Where do you get 1/3 from in explanation?

Question

Question #3 of 3Question ID: 1211840Cathy Moran, CFA, is estimating a value for an infrequently traded bond with six years to maturity, an annual coupon of 7%, and a single-B credit rating. Moran obtains yields-to-maturity for more liquid bonds with the same credit rating:5% coupon, eight years to maturity, yielding 7.20%.6.5% coupon, five years to maturity, yielding 6.40%.The infrequently traded bond is most likely trading at:A) par value.B) a discount to par value.C) a premium to par value.ExplanationUsing linear interpolation, the yield on a bond with six years to maturity should be 6.40% + (1 / 3)(7.20% – 6.40%) = 6.67%. A bond with a 7% coupon and a yield of 6.67% is at a premium to par value.(LOS 44.e)

Sophie Macon · Answer

Hi @pcunniff , for the comparable bonds, one is 5 years to maturity, and the other is 8 years to maturity. So that's 3 years difference.Given that the illiquid bond we are trying to compare is 6 years to maturity (1 year extra from 5 years to maturity), that's where you get 1/3.Does this make sense?