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Loan Repayments (Series) Help! (1 Viewer)
- Thread starter SGSII
- Start date
darlking
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- Feb 2, 2012
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Hi :>
In the first year, A1, the amount will be what you borrowed, $3000, PLUS interest (0.22) MINUS PAYMENT
>>>
A1= 3000(1+0.22)-M
= 3000(1.22)-M
In the second year, A2, the amount will be:
>>>
A2= A1(first year amount) X (1.22) - M
= [3000(1.22)-M](1.22)-M
As you can see here, you only expand 1.22 and NOT the -M as well. So you will get:
A2 = 3000(1.22)^2-M(1.22)^1-M^0
You will soon see a pattern. Can you see how, when it is A2(amount number 2 in the second year), the power to 3000(1.22) is 2 aswell? THEN it decreases to 1 then 0?
So fast forward.. if it was A5:
>>>
A5= 3000(1.22)^5-M(1.22)^4 - M(1.22)^3 - M(1.22)^2 - M(1.22)^1 - M^0
Got it? Also you will begin to see a GEO. series forming FROM M(1.22)^4
>> I factorise the M out
3000(1.22)^5 - M[1.22^4 + 1.22^3 + 1.22^2 + 1.22^1 + 1]
SWAP it around so 1 is in front and 1.22^4 is at the back and sub in to Sn= a(r^n-1)/ r-1
as a=1, r= 1.22 and n= 5
So it will look like THIS:
3000(1.22)^5 -M[1(1.22^5-1)/1.22-1)
and then just solve for M.
The answer should be $1047.62 !
Happy dayz
In the first year, A1, the amount will be what you borrowed, $3000, PLUS interest (0.22) MINUS PAYMENT
>>>
A1= 3000(1+0.22)-M
= 3000(1.22)-M
In the second year, A2, the amount will be:
>>>
A2= A1(first year amount) X (1.22) - M
= [3000(1.22)-M](1.22)-M
As you can see here, you only expand 1.22 and NOT the -M as well. So you will get:
A2 = 3000(1.22)^2-M(1.22)^1-M^0
You will soon see a pattern. Can you see how, when it is A2(amount number 2 in the second year), the power to 3000(1.22) is 2 aswell? THEN it decreases to 1 then 0?
So fast forward.. if it was A5:
>>>
A5= 3000(1.22)^5-M(1.22)^4 - M(1.22)^3 - M(1.22)^2 - M(1.22)^1 - M^0
Got it? Also you will begin to see a GEO. series forming FROM M(1.22)^4
>> I factorise the M out
3000(1.22)^5 - M[1.22^4 + 1.22^3 + 1.22^2 + 1.22^1 + 1]
SWAP it around so 1 is in front and 1.22^4 is at the back and sub in to Sn= a(r^n-1)/ r-1
as a=1, r= 1.22 and n= 5
So it will look like THIS:
3000(1.22)^5 -M[1(1.22^5-1)/1.22-1)
and then just solve for M.
The answer should be $1047.62 !
Happy dayz
Last edited: