Excel 2013 =SUM Formula. Utterly Stumped

Every year a local organization needs a spreadsheet put together to keep track of who paid what and when, and for the past few years my mom has done this. After how much the old document has bloated, it has become nearly unusable, so I was tasked with rewriting it. The use of the formulas was wrong, and did not actually calculate the total balance due, so I had to rethink the way things were calculated.

Most people make multiple payments and each one has to be put into different lines. The way I wrote it does not calculate it the way I intended, as I originally only tested it with a single line. I know this is an error I am making in terms of order of operations, but I'm not sure what to do to fix this.

This is a screenshot of my test document, the formula in the top is the one for the "Total Balance Due", which should equal $0 in the first group of lines.

Any help would be much appreciated, as I have tried google-ing for the past hour, but haven't found anything useful.

Have you tried this?

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Thank you @Meekoman25, you have just saved me hours of pondering. It worked like a charm!