A credit card has an annual interest rate of 20,99%, and interest charged is calculated at the end of the billing cycle. The minimum payment on the credit card is the greater of $20 or 2% of the unpaid balance. At the beginning of a 30-day billing cycle, the unpaid balance was $950 and purchase of $57, $75 and $113 were made respectively on days 12, 15 and 24. Moreover, a purchase of $550 was made on the last day and $355 was credited to the account on the day 24. 

1. Calculate the unpaid balance at the end of the cycle. 

2. Determine the interest charged in this billing cycle. 

3. At the end of the billing cycle, determine the new balance at the beginning of the next cycle, given that the minimum payment has been paid.