Sorry this is a bit late, but I may be able to help!

Bottom line before and if you get confused: you are doing/thinking about this 100% correctly.

This equation shown in the picture is actually not compound interest, that formula is P times (1 + r/n)^n*t, this is exponential increase, which is P(1+r)^t. 

Of course, as you said, the 1 in the formula represents the principal before the addition of R. And that is exactly what it is supposed to be! The picture does explain it like that, but in a different way. In the picture, it states that the formula can be written as the number (350), plus the added portion, (350 x .04), which is R. In the second part, the picture then says that we can combine the two parts of the equation (350, or 350 x 1), and 350 x .04, to 350 x 1.04, to get the same answer. Either way, whether you add the P x 1 and P x .04, or if you combine them to make P x 1.04, they will get the same answer.

Another example would be 500 times 1.04. 500 times 1.04 is 520. You could also write it as 500 times 1 (500) plus 500 times .04 (20), and you would still get the same answer.

The rule at the bottom says that basically if you want to get the sum plus interest, you basically have to multiply the principal by whatever extra percentage you need to add.

Hope this helps! If you have any other questions, just ask and I will answer! :) And if I can't answer them, definitely go to your math teacher for advice!

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