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According to this Derive Perpetual Bond Price , I learned how to derive the formula of perpetual bond. However, I still have some questions.

Firstly, do I need to change the formula when valuing the perpetual bond between the coupon dates. For example, if the settlement Date T is between the coupon dates T1 and T2

Do we need to change the formula such as,

Secondly, for Cumulative Perpectual Bond. If the issuer didn't pay the interest on the previous coupon date, that is T1, do we need to take that into account?

What's the market standard to quote the perpetual bond for this case.

Thanks.

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