How to calculate Amorized cost when no upfront is paid?

The amortized cost essentially spreads the recurring charges evenly across the billing period, regardless of whether there was an upfront payment or not. For example, if your billing period is a month (30 days), and the total recurring charges for the month were $100, the amortized cost per day would be:

Amortized cost per day = Total recurring charges / Number of days in billing period
                       = $100 / 30 days
                       = $3.33 per day

If you need the amortized cost for a week (7 days), you would then calculate:

Amortized cost for a week = Amortized cost per day × Number of days in a week
                           = $3.33 × 7 days
                           = $23.31

Regarding your question about getting the reports via API, AWS does provide a Cost Explorer API that you can use to fetch cost and usage data programmatically. This might be an alternative way to retrieve the amortized cost data if you're unable to calculate it from the exported data.