Monthly Repayments (1 Viewer)

[Cookie182]

Who is confident with bullshit like this-

$15000 borrowed at 12% p.a., money payed back at monthly intervals over 5 yrs. Find the monthly installment.

I kinda get how to do it- but as u can see it is a long method-

Let 'm' be the monthly payment

n = 5 x 12 = 60 months

monthly interest = 1 %

After 1 Month>

A1= 15000(1+1/100)^1 - M
= 15000(1.01)^1 - M

A2= A1(1.01)^1 - M
= [15000(1.01)^1 - M](1.01) - M
= 15000(1.01)^2 - M(1.01+1)

A3= A2(1.01) - M
= [15000(1.01)^2 - M(1.01+1)](1.01)- M
= 15000(1.01)^3 - M(1.01^2 + 1.01 +1)

A60= 15000(1.01^60- M(1+1.01+1.01^2+1.01^3+...1.01^59) (Latter part is our geo series with a=1, r= 1.01 and n=60)

Sum of series-

S60= 1(1.01^60-1)/(1.01-1)

Therefore, A60 = 15000(1.01^60- M(1(1.01^60-1)/(1.01-1))

If loan is repaid after 60 months, then A60 = 0

therefore,

15000(1.01^60- M(1(1.01^60-1)/(1.01-1))=0

M(1(1.01^60-1)/(1.01-1))= 15000(1.01)^60

Finally,

M= 15000(1.01)^60(0.01/(1.01^60 -1))

Therefore the monthly repayment is $333.67 or $334 dollars.

Fucking long and confusing

There is a much quicker way using the formula-


PR^n = Q(R^n -1)/(R-1) where Q is the 'installment' but it looks as though we need to know how to do these questions with a geometric series appraoach. Praying we dont get one this yr!!!

 

[watatank]

if you do it the way you're doing it, you aren't wrong. the formula only applies if the payment terms don't change.

 

[Starcraftmazter]

You have to do it the long way, it's in the silly-bus.

I am *assuming* we won't get one, because it would be an impractical question.

 

[wrxsti]

You have to do it the long way, it's in the silly-bus.

I am *assuming* we won't get one, because it would be an impractical question.

lolololololol. i love the
(Excuse for not comming first in extension maths... very hard subject)

for the question,
If they do ask it.
They will give it in parts
eg)
a) Find A1

b) Find ammount remaining after the "nth" repayment.

c) If loan is repaid after 6 years, find the ammount of each repayment.

d) Find total ammount of interest paid.

e) wrxsti is so smart

 

[Starcraftmazter]

I was just thinking about parts, but I couldn't figure out how to split up a question like that into parts, so I guess you are indeed smarter than me

 

[crono26]

i just wroked it out...
a=150000
n=60
r=1.01
sub all that into the formula
150,000(1.01^60) - $M ((1.01^60)-1) x (0.01) / (1.01 -1) = 0

and then solve for m
you get $3336 monthly

your answer cant be right.. if he borrows 150,000 and he's paying 1% a month then the answer is going to have a total greater than 150,000...approx 200,000

and 3336x60 = 200,160 which is alot closer
your answer of 334 only makes about 20 grand... so clearly isnt right

EDIT:
fuck.. just realised it was 15,000
your answer is correct (same as my new one)
good luck!