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I am trying to find a formula that will let me calculate what percentage my money will need to grow at to reach my goal at the end of ten years, if I start with a certain amount and keep contributing a set amount to that portfolio for each month over the ten-year period.

What you're looking for is called a "time value of money" calculation. Unfortunately, calculating TVM is not easy, and you need a specialized business calculator (or computer application) to do so with any reasonable ease. There are some such calculators online, though. For example,
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