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Why is it true that the value of a floating rate loan is equal to its par value at payment dates?

How can one show this mathematically? I want to understand this both conceptually and mathematically.

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On every reset date, coupon rate is reset to current market rate & as we know that bond trades at par when coupon and market rates are same.

Mathematically, we just need to substitute coupon rate with market rate to price a bond on the reset date.

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  • $\begingroup$ I don't quite understand your response. Can you please elaborate? Thanks $\endgroup$ – Frank Swanton Nov 7 '19 at 15:27

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