Chapter 3.1, Problem 84E

In Problems $83\text{-}86$, assume that the annual interest rate on a credit card is $19.99\%$ and interest is calculated by the average daily balance method.

The unpaid balance at the start of a 30-day billing cycle was $\text{\$1,583}\text{.44}$. No purchases were made during the billing cycle and a payment of $\text{\$1}\text{.583}\text{.44}$ was credited to the account on day 21. Find the unpaid balance at the end of the billing cycle.