Formula for credit card balance as a function of payments

[barryj]

I have been trying to find the financial formula that will give the balance of a credit card debt as a function of time. Example, at 18% interest, if I pay $150 a month how long will it take me to pay off my debt. When I google, I get pointers to Excello functions. I want to know the exact formula.

 

[jedishrfu]

Try looking for the compound interest calculation.

I found this discussion on it:

https://en.m.wikipedia.org/wiki/Compound_interest

 

[BWV]

It all comes from the basic formula for an annuity

In your case the PV is the loan balance, P the payment, r the rate and n the number of periods - so you need to solve for n, so it’s easier to just iterate

 

[pasmith]

It all comes from the basic formula for an annuity

In your case the PV is the loan balance, P the payment, r the rate and n the number of periods - so you need to solve for n, so it’s easier to just iterate

Taking logs is hardly difficult. $$n = \left.\log\left( \frac{P}{P - rPV}\right)\right/ \log(1 + r).$$ Having made $\lfloor n \rfloor$ payments, you will have one further payment of less than $P$ to make.

Solving for $r$ is the difficult one, as this is a polynomial of order $n + 1$ which cannot be solved analytically for $n \geq 4$ (although $r = 0$ is always a solution).