Self-study vs. Online class?

So, I maxed out of math options at school. I was supposed to be taking another AP math, but my school cancelled it at the last minute and I had already taken all the other courses. I wanted to take an online course through Keystone, but my parents were reluctant since it is 500 dollars. Now they are reconsidering.

My question is would it be the same if I put in the additional info section that I am self-studying for the exam or if I’m taking an online course? I don’t want to put any financial stress on my parents, so I would prefer not to take the class but I don’t want it to hurt my chances at top schools since without it my senior course load looks kind of light. I’m not sure in this case if adcoms would consider self-studying on the same level as taking an online Keystone course.

If you have taken all of the math offered by your high school, then no college in the country is going to expect that you bend yourself out of shape to find a math class somewhere else. Enjoy your math-free year.

There is no advantage in admissions to self-studying over taking an online course. You should take a course you have always wanted to take but didn’t have a chance to take before.

My son is in a similar position, so he is doing independent study classes this year. His school has a procedure for these - he had to submit a proposal and find a teacher to work with him - some are small group projects with 1 or 2 other students. He is using free online resources (MIT open courseware for one, a text book for another). See if the school district will cover the cost for the online class - some will provide resources if you have finished their curriculum - or allow an independent study with a current teacher.