Chapter 3.1, Problem 86E

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 $\text{\$475}\text{.17}$. A purchase of $\text{\$125}\text{.93}$ was made on day $3$.No payment was made during the billing cycle and a late fee of $\text{\$37}$ was charged to the account on day $25$. Find the unpaid balance at the end of the billing cycle.