We have an initial balance of $5500.
The APR is 24% and each month only 2% of the balance (the minimum payment) is paid.
An APR of 24% means an actual monthly interest rate of:
Then, the remaining balance each month will be increased by 0.02 or 2% because of the interest.
We also have to substract from the balance the 2% payment done every month.
Calculation of the first balance:
We start with a balance of $5500. It will generate an interest of 2% each month that is equivalent to 0.02*5500 = 110.
Then, the balance for the first month will be 5500+110 = $5610.
If we pay 2% of this amount, we pay 0.02*5610 = 112.2.
This will left a balance of 5610-112.2 = $5497.80.
Generalization:
We can calculate the balance for the first month, B(1), as:
We can replace i, the monthly interest rate, and p, the payment percentage, and rearrange this as:
Then, we see that each month the balance will be reduced to a 99.96% of the balance of the previous month.
Then, we can extrapolate this to any month as:
If we calculate the balance for the 30th month, we get:
Answer: the balance after 30 months will be approximately $5434.38