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In summary, the conversation was about finding the financial formula for calculating the balance of a credit card debt over time. The formula involves compound interest and the variables of loan balance, payment, interest rate, and number of periods. It was suggested to look for the compound interest calculation and to solve for n using logarithms. However, solving for r can be difficult for higher values of n.

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Try looking for the compound interest calculation.

I found this discussion on it:

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

I found this discussion on it:

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

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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

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BWV said:

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. [tex]

n = \left.\log\left( \frac{P}{P - rPV}\right)\right/ \log(1 + r).[/tex] Having made [itex]\lfloor n \rfloor[/itex] payments, you will have one further payment of less than [itex]P[/itex] to make.

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

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