Loan Repayments (Series) Help! (1 Viewer)

[SGSII]

Hi Guys
Could someone please explain the steps on how to do loan repayments using this as an example question:

I really dont understand the examples provided in the textbooks :S
Please help!
Thanks

 

[darlking]

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

 

[SGSII]

Thankyou soo much!!