otispunkmeyer
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Ok so its not a car related question, but I dont know where else to put it.
Have a look at this site:
http://mortgage-x.com/library/answers/amortization.asp
In particular, this part:
Now I worked through it and understood how the things expand out if you keep going. But I dont understand whats going on with this sum of the finite series.
The series is clearly from 1 (or a^n where n = 0) to a^n so, doing the manipulation I do agree with their result for the sum of the finite series being (1-a^(n+1))/(1-a)
What I dont get is why they then sub that back in and use it to represent the numbers up to a^(n-1).
1+i is basically a so they have LB = LB(0)*(a)^n - PMT(1 - a^(n-1))/(1-a)
I dont recall doing series where there are 2 different constants in the series and different signs for everything but the first number (essentially everthing in the brackets after PMT is negative). PMT and LB(0) are constants.
What am I missing here?
Have a look at this site:
http://mortgage-x.com/library/answers/amortization.asp
In particular, this part:
LB = LB(0)*(1 + i)^n - PMT*((1 + i)^(n-1) + ... + (1 + i) + 1)
The sum of the finite series: 1 + a + (a^2) + (a^3) + ... + (a^n) is (1-a^(n+1))/(1-a)
As it can be easily seen:
if SUM is the series sum, then SUM - a * SUM = 1 - a^(n+1)
solving for SUM:
SUM = (1-a^(n+1))/(1-a)
Now I worked through it and understood how the things expand out if you keep going. But I dont understand whats going on with this sum of the finite series.
The series is clearly from 1 (or a^n where n = 0) to a^n so, doing the manipulation I do agree with their result for the sum of the finite series being (1-a^(n+1))/(1-a)
What I dont get is why they then sub that back in and use it to represent the numbers up to a^(n-1).
LB = LB(0)*(1 + i)^n - PMT*(1-(1 + i)^n)/(1-(1 + i))
1+i is basically a so they have LB = LB(0)*(a)^n - PMT(1 - a^(n-1))/(1-a)
I dont recall doing series where there are 2 different constants in the series and different signs for everything but the first number (essentially everthing in the brackets after PMT is negative). PMT and LB(0) are constants.
What am I missing here?