I think, I'm not certain, that credit card companies ring up your balance immediately, so for payments made and purchases made, I'm assuming all interest charges are made immediately, and then the payment or purchase is considered after that. 30 days in June. We start with our balance of 4259.64. Roll that up with 10 days of interest:

4259.64*(1.00030822)^10 = 4272.79

Now subtract the payment out of the new balance:

4272.79 - 180 = 4092.79

Now roll up that balance 17 days later:

4092.79 * (1.00030822)^17 = 4114.29

I take this balance before the new purchase of 520.67 is made. Adding this new purchase on, we have 4634.96.

2 more full days of interest until the end of the month get us:

4634.96 * (1.00030822)^2 = 4637.81

Now, finance charge if we assume even weighting of time with payment and purchase gives us 4637.81 - original balance of 4259.64 = 378.17.

I researched this more, and we may need to add our payment back in of 180 and subtract our purchase of 520.67 to get 37.50 of true finance charge.

What does your answer key say?