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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A peculiar property of this is that the mortgage balance falls slowly at first and then it gradually picks up; it's just a property of this formula.

其中一个特别的性质是,刚开始抵押贷款余额降得很慢,渐渐的,越降越快,这就是这个公式的性质

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It's very important to understand that the mortgage balance is recomputed, according to this formula every month and they will send you a statement showing how your mortgage balance is falling.

根据这个公式 抵押贷款余额,每个月都要重新计算,理解这一点非常重要,他们会给你寄对账单,告诉你抵押贷款余额减少的情况

耶鲁公开课 - 金融市场课程节选

That's because, at the end, if- -suppose you're one month or two months away from the payoff of the mortgage, you don't have any balance left, so the interest that you're paying is -hardly any balance left--is very low and so you're payment is paying off principal, mostly.

这是因为,在最后,如果,假设你还剩1到2个月,就可以还清抵押贷款,那么剩下的贷款余额就很少了,因此你所需要付的利息,将会非常少,因为贷款余额几乎为零,此时你偿还的就主要是本金

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At every point of time your mortgage balance is equal to your mortgage payment times that square bracketed thing, where T is the amount of time you have left.

在每个时间点的抵押贷款余额,都等于每月偿还额乘以,方括号内的值,T是剩余年份数

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