geometric progression

R

red and white kop!

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Jun 15, 2009
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im not sure where to post this
so
a bank loan of 500 pounds is arranged to be repaid in two years by equal monthly instalments. Interest, CALCULATED MONTHLY, is charged at 11% per annum on the remaining debt. Calculate the monthly repayment if the first repayment is to be made one month after the loan is granted.

I've been working for almost two hours on this problem, ending up with the equation (500-m)(1211/1200)^24 - (1200m/11) ((1211/1200)^24 -1)
m being the equal monthly repayment
from there i ended up with m= 21.something, apparently not far from the truth but nevertheless incorrect; can somebody show me how they would do this?
 


Here's a formula for calculating the monthly payment R on a loan amount A with n monthly payments and interest rate per time period i.

R = Ai/[1 - (1 + i)^(-n)]

11% is the rate per year.

11%/12 is the rate per time period (i.e., month).

I get a monthly payment of $23.30 8-)

 
yeah but i dont know that do i
im studying sequences so i need related explanations, like using Sn (in a GP) = (a (1-r^n))/ (1-r)
r being the common ratio and a the first term obviously
 
abovementioned! how would you incorporate that formula for the sum of a geometric series? is my mid-problem equation correct? should i use n=24 or 23, seeing that no interest would be paid on the last sum?
 
red and white kop! said:
yeah but i dont know that do i
Click to expand...
You don't know WHAT?
Mark gave you the formula that gives the monthly payment given amount borrowed, rate and number of payments.
What else do you want? What are you after: HOW the formula works?
The formula is simply a combination of the future value of the amount borrowed,
and the future value of the payments, which must equal each other.
 
im not doing finance math kiddo, i have not been taught that formula and threfore i must utilize another formula related to geometric progression which is what i am studying
is that clear enough for you?
 
ok so i got 23.29 when my textbook says 23.31; is this a negligible difference or a symptom of a BIG problem? this is my work
ahem
S1= (500-m monthly payment) x (1211/1200)
S2= (S1 -m) x (1211/1200)
= (500-m)(1211/1200)^2 - (1211/1200)m
and so on
so i take as general equation for finding m
0= (500-m)(1211/1200)^24 - m[(1211/1200)^23 -1]/[(1211/1200)-1]

from there i get 23.29 pounds
is there any fault in my working?
 
red and white kop! said:
ok so i got 23.29 when my textbook says 23.31; is this a negligible difference or a symptom of a BIG problem?
S1= (500-m monthly payment) x (1211/1200)
S2= (S1 -m) x (1211/1200)
= (500-m)(1211/1200)^2 - (1211/1200)m
and so on
so i take as general equation for finding m
0= (500-m)(1211/1200)^24 - m[(1211/1200)^23 -1]/[(1211/1200)-1]
from there i get 23.29 pounds
is there any fault in my working?
Click to expand...
23.30 is the actual answer: 23.3039...
NO faults in your working: BUT what you got is EXACTLY the SAME as what you've been given
by me and Mark, in different style...so what is it you're complaining about?

Take your example of 500, but to illustrate I'll make rate 12% and number of months = 5
Since 1212/1200 = 1.01, I'll use 1.01 (less typing!).
Code: 
500(1.01^5)        =               p(1.01^4) + p(1.01^3) + p (1.01)^2 + p(1.01) + p
(1.01)500(1.01^5)  =  p(1.01^5) +  p(1.01^4) + p(1.01^3) + p (1.01)^2 + p(1.01)

(1.01)500(1.01^5) - 500(1.01^5) = p(1.01^5) - p
Solve for p: p = 103.0198...

There ya go, all wrapped up with your beloved geometric series :wink:
 
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