What this equation merely says is that the present value of your remaining payments is always equal to the mortgage balance.

这个等式说明了,剩余偿还额的现值,就等于抵押贷款的余额

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This is the present value of $1 in one time period, which I'm taking to be a year.

这就是一美元在一段时期内的现值,我只是将一美元持有一年

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So, they are selling widgets or whatever and making money-- the value of the company is the present value of that cash flow.

不管通过什么方式赚钱,即便卖小商品...,公司的价值等于现金流的现值

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What is the present value of that? Well, the first-- each payment we'll call a coupon-- so it pays one pound one year from now.

那么它的现值又是多少呢,首先,每一次支付的数额称为一个券息,从现在开始每一年都要支付一英镑

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Then you want to add the present value of the principal and that's the formula.

最后还要加上债券面值的现值,这就是债券定价公式

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Then the present value of $1-- The present PDV or PV of $1 = $1/.

一美元的现值...,一美元的现期贴现值或者现值就等于1/

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The present value is equal to-- remember it starts one year from now under assumption-- we could do it differently but I'm assuming one year now.

则现值就等于,记住它从现在开始起一年一年的支付,只是个假设,我们能做不同的假设,但现在我就假设成一年

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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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The present value is what that's worth today.

现值就是指它在今天的价值

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What is the present value of an annuity?

那么年金的现值又是什么呢

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The present value of this--suppose it pays-- let's say it pays c pounds each year, so it would be c times this.

它的现值就是...假设它需要支付,我们假设它每年支付c英镑,然后这里也乘以c

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This point here then is the present value of your income; it's Y today + / .

直线与x轴的交点表示收入的现值,它等于

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The price is just the present value of that stream, discounted at the interest rate.

债券的价格就是这些现金流,以利率r为贴现率算出的贴现值

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Generally, if it pays c dollars for every period, the present value is c/r.

推广开来,如果在每段时期内支付c美元,那么它的现值就是c/r

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It would be c times 3 in the third year, etc., Then the present value is equal to c/-- that's the formula for the value of a growing console.

在第三年它就是三倍的的三次方,现值就相当于c/,这就是上涨债务价值的公式

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You want to subtract off the value of a perpetuity that starts after 2T, six-month intervals, so this is the present value of the perpetuity that starts after 2T, six-month intervals.

所以就要从永续债券价格里减去,2T期以后,每六月一期券息的贴现值,这部分是永久债券从第2T期后,每半年一期券息的现值

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I'll give you the present discounted value for it."

我会给你个现期贴现价值

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