How do I convice my sister that I did not steal from her graduation money?

Okay. So I have a slightly checkered past. By this I mean I have been guilty of taking money from my brother before. But. Before you go and tell me that it is wrong and how could you do such a thing, I know this. I know that it is not right and it is not moral. I know that I never should have done it in the first place. I am VERY guilty and embarrassed for what I did to him, and I have since paid him back and things in regards to that situation are good.

Yesterday, my sister and I went out shopping to look for accessories for her laptop. She brought approximately $200 with her, and she said today that $60.00 is missing. I trust her judgement in that there is money missing, but I know she thinks I did it. She will not talk to me even though I have let her dig through my purse and look at my bank register that shows there wasn’t a deposit yesterday. She’s looked everywhere I could possibly hide money and hasn’t found anything, and with good reason: I DIDN’T TAKE IT. I just know she doesn’t believe me or is having a very hard time believing me. And, of course, I don’t blame her for that, either.

I just would like some advice on how to handle this situation. Of course, I am the prime suspect, that is if she didn’t somehow miscount her money or if she didn’t drop it, etc. We’ve gone over multiple scenarios.

I’m just sick to my stomach because I don’t want to lose her as a friend. I don’t want to lose her trust over something I didn’t do, you know?

How would I explain this to her?

Thank you! :)