How to calculate credit card repayments

StarBurst_3

I was wondering if anyone can help me. I'm trying to find out what the formula is for calculating the the length of time and the total cost to pay off a credit card if I know the outstanding debt, the interest rate and assume the minimum monthly payment at 5%. I know there are lots of web calculators out there but I'm trying to understand the formula on paper.

Thanks

CLAPTON

It will of course take for ever if you are paying 5% of the balance each month because however small the balance you will always leave 95% behind. In practice of course CC always have a mimimum payment so once its about e.g. £5 the total is paid off.

basically you can work it out like this

assume you owe A
monthly interest rate is m ( as a decimal)
repay rate is p (as a decimal i.e 5% is written as 0.05)

then:
at the end of the first month the amount outstanding is:-
borrowed amount plus interest less payment i.e.

A(1+m) - A(1+m) x p = A(1+m) x (1-p)
after two payments it works out as A (1+m)power 2 x (1-p) power 2

so after n monthly payments you still have
A((1+m)power(n) ) x (1-p)power(n) left to pay
so once you determine the point where you pay it off in total the value of n tells you have many payments you have made.

The first payment is
amount owed x interest rate
i.e.
Ax(1+m) x p

second payment is amount now owed times interest rate is
Ax(1+m) x(1-p) x (1+m) x p

etc

so for nth payment (rearranging terms etc)
is
Ap/(1-p) x (((1+m)x(1-p) power(n))

Adding up each of the payments you get

writing y= (1+m) x (1-p) for convenience
Ap/(1-p) x ((y-ypower(n+1)))/(1-y)



So the conclusion is that only paying the minimum amount each month is seriously silly.

StarBurst_3

Superb - thanks for that!

Squirrel29

Blimey... you should be changing your username to Prof. Clapton:rotfl:

wyebird

Hmmmm...note to self...read post properly