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
Now. I want to move away from statistics and talk about present values, which is another concept in finance that is fundamental.
好的,讲到这里我将离开统计学,讨论一下现值,这是金融学中的另一个基本概念
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
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
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
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
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/
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
We have formulas for these present values and these formulas are well known.
我们有几个公式,来计算现值,这些公式相当有名
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
The present value is what that's worth today.
现值就是指它在今天的价值
What is the present value of an annuity?
那么年金的现值又是什么呢
What is a present value?
现值是什么
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
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
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
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
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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