Question

What is the total cost to repay a credit card loan with a balance of $25,000, an APR of 15%, and a minimum monthly payment of $330?

Answer 1

how long does it take to pay it off?

Answer 2

you got any formula for telling you the current balance of a loan?

Answer 3

sorry, no

Answer 4

it would be useful if you had some formula that could tell you such things.

Payment formula is to ... ugh

Any present value or future value formulas ?

Answer 5

i have one that i developed during accounting class, the text books were giving all sorts of formulas and so i just developed my own that pretty much combined them all

Answer 6

what is it?

Answer 7

spose you have balance, B, compounding at some rate, k, over n periods

Bn = Bk^n

now spose the balance changes due to some regular payment, P. The sum of the payments made follow a geometric series whose sum is the formula:

(k^n-1)/(k-1)

therefore, lets subtract our payments as

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

when Bn = 0, the loan is paid right?

Answer 8

...I think so...

Answer 9

do we like paying loans after they get to a 0 balance? of course not :)

Bn=0 is the loan paid in full

so we just solve for n to know how long it takes

Answer 10

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

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

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

0 = Bk k^n - Bk^n - Pk^n -1

0 = k^n(Bk - B - P) -1

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

log(1/(Bk - B - P)) = n log(k)

- log((Bk - B - P))/log(k) = n

Answer 11

the total cost of the loan is n*P

Answer 12

...so confused

Answer 13

im not a mind reader so youll have to express that confusion in a manner that i can actually aid in.

Answer 14

do we have a formula developed to find the total number of payments needed?

Answer 15

what the heck are 'b' and 'p' and 'k' and 'n'?????

Answer 16

i defined them clearly in the postings

balance, payments, number of periods, an compounding interest

Answer 17

as previously posted above:
_____________________________

spose you have balance, B, compounding at some rate, k, over n periods

Bn = Bk^n

now spose the balance changes due to some regular payment, P. The sum of the payments made follow a geometric series whose sum is the formula:

(k^n-1)/(k-1)