The simplest thing is something called a consol or perpetuity.

其中最简单的东西叫做公债或叫永续年金

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There have also been one hundred-year bonds and there have also been perpetuities that-- in the UK, for example, the British Consoles-- have no expiration date and they have infinite maturity.

还有更长期的一百年债券,还有一种永续年金,比如说英国的大英统一公债,没有过期日,永不到期

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That's the formula for the present value of a consol.

它就是永续公债里现值的计算公式

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It's not forever because it terminates after 2T periods of six-month interval each.

债券不是永续的,券息每六个月为一期,共支付2T期

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If you had a perpetuity, which paid C/2 forever, you already know from the perpetuity formula that the value of that would be C/2 divided by r/2 if r/2 is the discount rate.

如果你有一只永续债券,每半年付息C/2,没有到期日,从永续债券的公式可以知道,债券价格等于C/2除以r/2,r/2为贴现率

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