Answer:
- paid on balance: $128.70
- credit card company profit: $59.19
Explanation:
Given an initial credit card balance of $650, a payment of $21.45, and an APR of 19.85%, you want a payment and balance schedule for the first 6 months of the payoff.
Payment
The term "payment" can refer to the amount paid to principal over and above the finance charge, or it can refer to the amount of the check written to the credit card company, including the finance charge. Often, the former interpretation is the one that is associated with the wording "minimum payment."
Equations
Using the idea that the "payment" is the amount by which the balance is reduced, the attached table shows the finance charges and balances for the first 6 months.
In each case, the interest is ...
interest = (0.1985/12)·balance . . . . rounded to cents
The total payment is ...
total payment = $21.45 + interest
The new balance (amount remaining) is ...
new balance = balance + interest - total payment
Amount paid off
Since $21.45 each month goes to the principal, the amount paid in 6 months is ...
6×$21.45 = $128.70
Credit card earnings
The credit card company earned an amount equal to the total of interest payments in the first 6 months:
$10.75 +... +8.98 = $59.19
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Additional comment
The math in these problems is repetitive and can be tedious. It is best handled by a spreadsheet, which can duplicate the formulas as many times as required. Rounding to cents is a spreadsheet function easily incorporated into the formulas.
If $21.45 is the total payment amount, then the amount by which the balance is reduced each month is the difference between that payment amount and the interest due. The payoff will be much slower, and the credit card company earnings will be somewhat higher. The revised formula for the spreadsheet is ...
total payment = $21.45