Jim starts with a $2000 balance on his credit card. During the first month he charges $300, and during the second month he charges $500. The credit card has finance charges of 23% APR. The first month Jim makes a $200 payment and the second month Jim makes a $400 payment. What is the balance at the end of the second month?
To calculate the balance at the end of the second month, we need to start with Jim's initial balance and then take into account the charges, payments, and finance charges.
1. Start with Jim's initial balance of $2000.
2. Add the charges for the first month. Jim charged $300, so the balance after the first month's charges is $2000 + $300 = $2300.
3. Subtract the payment for the first month. Jim made a $200 payment, so the balance after the first month's payment is $2300 - $200 = $2100.
4. Calculate the finance charges for the first month. We'll use the annual percentage rate (APR) of 23% to calculate the monthly finance charge. First, convert the APR to a monthly interest rate by dividing it by 12: 23% / 12 = 0.0192. Then, calculate the finance charge for the first month by multiplying the balance after the first month's payment by the monthly interest rate: $2100 * 0.0192 = $40.32. Add this finance charge to the balance: $2100 + $40.32 = $2140.32.
5. Add the charges for the second month. Jim charged $500, so the balance after the second month's charges is $2140.32 + $500 = $2640.32.
6. Subtract the payment for the second month. Jim made a $400 payment, so the balance after the second month's payment is $2640.32 - $400 = $2240.32.
7. Calculate the finance charges for the second month. Using the same monthly interest rate of 0.0192, the finance charge for the second month is $2240.32 * 0.0192 = $43.01. Add this finance charge to the balance: $2240.32 + $43.01 = $2283.33.
Therefore, the balance at the end of the second month is $2283.33.