Clarification reqd- interpolation in sfm

Hi All,   In page number B.7 in supplementary study material of CA Final SFM, In problem number 51 from Chapter 6, How are the two rates 7.5% and 9% for interpolation is arrived at after the below equation:                                        7*PVIFA(YTM,10) + 100*PVIF(YTM,10)=90

 

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these two rates are nothing but an assumption based on current yield %, you may assume any other rates!

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