# loan repayment question help. (1 Viewer)

#### marann

##### New Member
could sombody PLEASE help me with this... workin out would be much appreciated 8. When justin borrows \$8500 and 12%pa over 5 years he does not have to make any repayments for the first 2 months.

a) how much does he owe after 2 months?
b)what is the amount of each monthly repayment?
c) how much does he pay back altogether?

a)\$8670.85
b)\$197.75
c)11469.21

#### hur91

##### New Member
A) interest is 12% p.a., calculated monthly, so we divide that by 12 and the rate becomes 1% or 0.01
After one month, he owes 8500 plus interest
A1= 8500*(1.01)
After two months he owes A1 plus interest
A2= A1*(1.01)
= 8500*(1.01)*(1.01) [where * equals multiplied by]
= 8670.85

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#### hur91

##### New Member
B) After 2 months he owed
A2= 8500(1.01)^2
Now, in the 3rd month, he has to start his repayments, so far the loan was just building up

Let his monthly repayment be M
After 3 months he owes:
A3= A2*(1.01) - M
= 8500*(1.01)^3 - M

After 4 months:
A4= (8500*(1.01)^3 - M)*(1.01) -M
= 8500*(1.01)^4 - M*(1.01 + 1)

Hence you can see a pattern forming, so for the 60th month:
A60= 8500*(1.01)^60 - M*(1.01^57 + 1.01^56 + ....... + 1)

In the 60th month, the loan should be paid off:
A60= 0
Therefore,
8500*(1.01)^60 - M*(1.01^57 + 1.01^56 + ....... + 1) =0

(1.01^57 + 1.01^56 + ....... + 1) is a series.

now all you have to do is find the sum of the series and do a little rearranging and you get the answer

M= 197.745

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#### hur91

##### New Member
C) You know how much he owes per month, that is the answer of B)
Just multiply that amount by the number of months.
197.745 * 58
I get \$11466.21 per month

PS, havent done this for a while, if anyone finds any probs with it, pls point out #### jimmysmith560

##### New Member
Thank you so much for the help. I am posting this literally 10 years after the original post but I have to say it was worth looking for the question online. 