Tran has a credit card with a spending limit of $2000 and an APR (annual percentage rate) of 12%. During the first month, Tran charged $450 and paid $150 of that in his billing cycle. Which expression will find the amount of interest Tran will be charged after the first month?

To find the amount of interest Tran will be charged after the first month, you can perform the following steps:

1. Determine the average daily balance. 2. Calculate the daily periodic rate (DPR). 3. Compute the monthly interest.

Step 1: Average Daily Balance Since Tran charged $450 and paid $150 within the billing cycle, assuming there were no other transactions, the average daily balance would typically be calculated based on the balance each day. If the charge was made on the first day of the cycle and the payment at the end of the cycle, the average daily balance would be close to $450, as the $150 payment would only affect the balance on the last day.

For simplicity, let’s assume that the average daily balance is $450 for the entire monthly cycle.

Step 2: Daily Periodic Rate (DPR) The APR is 12%, but we need to find the DPR because interest is applied daily.

DPR = (APR / 100) / 365 DPR = (12% / 100) / 365 DPR = 0.12 / 365 DPR ≈ 0.000328767

Step 3: Compute the Monthly Interest Finally, we multiply the DPR by the average daily balance and the number of days in the billing cycle to get the monthly interest charge. Assuming the billing cycle is 30 days:

Monthly Interest = DPR * Average Daily Balance * Number of Days Monthly Interest = 0.000328767 * $450 * 30 Monthly Interest ≈ $4.43

So, the expression to find the amount of interest Tran will be charged after the first month is: 0.000328767 * $450 * 30 ≈ $4.43

Please note that this calculation assumes a simple interest calculation without compounding and that interest is calculated on the average daily balance. Credit card companies might compute interest daily and add it to the balance which then compounds over the month.