Question

You have a credit card with an existing balance of $1,569.34, a credit limit of $2,000, and an interest rate of 12.5% APR. You pay $150.00 a month. When will the balance be below the target debt ratio to improve your credit score?

Answer 1

@ganeshie8 Can you help, please?

Answer 2

if i knew what the target debt ratio was ....

Answer 3

Well it said under 50% for me, but I just couldn't seem to figure it out?

Answer 4

if you make no new purchase then we can determine a new balance from the old balance/payments made using a formula.

Answer 5

Bn = Bk^n - P(1-k^n)/(1-k)

where k is a compounding term: (1 + apr/12) and n is the number of months

Answer 6

Uhm..Alright, I think.

Answer 7

does 50% mean that we want a balance of 100 or less?

Answer 8

1000 that is

Answer 9

They want you to never have a debt ratio of more than 50%

Answer 10

1000 = 1569.34(1+.125/12)^n - 150(1-(1+.125/12)^n)/(1-(1+.125/12))

and solve for n

lets see if its less clutter to do a general solution then plug in the specifics

Answer 11

I'm sorry, I'm really confused.

Answer 12

working a formula to solve for variable is all we are doing. if you have your own formula to work with thats fine, i just tend to use the one im familiar with

Answer 13

No, it's fine. I don't really know what to do with it -- I'm just really bad with numbers. My apologies.

Answer 14

Bn = Bk^n - P(1-k^n)/(1-k)

Bn (1-k) = Bk^n (1-k) - P(1-k^n)

Bn (1-k) = Bk^n (1-k) - P +Pk^n

Bn (1-k) = k^n [B(1-k) +P] - P

Bn (1-k) +P = k^n [B(1-k) +P]

[Bn (1-k) +P]/[B(1-k) +P] = k^n

log both sides

log[Bn (1-k) +P]/[B(1-k) +P] = n logk

log[Bn (1-k) +P]/[B(1-k) +P]
------------------------- = n
logk

Answer 15

now plugging in our numbers should give us a solution to n, the number of months it will take

(log(1000(-.125/12)+150)-log(1569.34(-.125/12)+150))/(log(1+.125/12))

http://www.wolframalpha.com/input/?i=%28log%281000%28-.125%2F12%29%2B150%29-log%281569.34%28-.125%2F12%29%2B150%29%29%2F%28log%281%2B.125%2F12%29%29

with any luck thats typed in correctly :) and gets us to about 4 months, little over

Answer 16

we can work it out in a spread sheet to see how the payments and such are stacking up for us

Answer 17

end balance = beg balance(interest) - payment

Answer 18

Sorry! Openstudy crashed and I just now got it back.

Answer 19

yeah, its been being a pain for months now i believe.

Answer 20

I've always had trouble with it..I think I get what you did, at least enough. Thank you so much for your help.

Answer 21

youre welcome, good luck :)