00:01
So the concept that i would use here is present value, right? and the present value says, right, suppose you took one million or you took 10, took 10.
00:17
Could you pay yourself, right? could you pay yourself 12 by 1 over time? right? so that's the question.
00:34
We are thinking about how much these things are worth, right? well, how much the question then becomes, right? well, how much will you need? well, how much will be needed to do this, right? if i'm thinking about, can i take the 10 million, invest it, earn interest, and pay myself the 1 million for each of the next 12 years, how much am i going to need? well, let's think about this in year one.
01:05
In year one, i need x, right? and i need x and i'm going to earn one plus r, right? so this is what i need.
01:19
And that needs to give me one million, where r is the rate of interest, right? this tells me if i get r today, i invested for a year at rate r, i will get a million dollars a year from now.
01:41
That tells me how much i need today, right? me the present value.
01:46
For year two, right, i would get to invest x, right? but i would get to earn our twice, right? and so on and so on and so forth.
01:55
Right.
01:56
So for each of these things, i need a different value of x because as the time to pay gets further and further and further away into the future, let's call it x1 and x2, the amount that i need today is getting smaller and smaller and smaller because i have more and more and more years to earn interest on it.
02:18
So if we kept doing that, right, in total, the total need would be 1 over 1 plus r plus, right? one over 1 plus r squared plus dot, dot, dot, plus one over one plus r to the 12th, right? this would be my x1...