Interest rate immunization - duration matching

Hi guys,

I have a question regarding the formula on Reading 23 section 4.2 Duration matching. I will copy paste the passage as others might search for it.

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I appreciate if you explain the calculations on the last sentence. I wasn’t sure how the denominators 4.5, 5.5 and 5.5 are calculated. The numerators are easy and most probably the difference between the reference point (6 year) and the related yield.

Thanks so much…

4.5 = 6 − 1.5

5.5 = 11.5 − 6

It’s simple, linear interpolation.

Thank you mate! I think i will be able to figure out the rest, “linear interpolation” is the key. Cheers.