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How does a bond has a non-integer time to maturity? (maybe the settlement date is between two coupon date?) and how do we calculate the

How does a bond has a non-integer time to maturity? (maybe the settlement date is between two coupon date?) and how do we calculate the current bond price if we only have information about current coupon number (not date), numbers of coupon remaining, time to maturity (not integer) and face value?

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