Why 5% is equal to multiplying by 1.05?

Multiplying by one makes no difference in the final result. Depending on whether you want to emphasize something, you could say "the original amount" or "the entire original amount". Multiplying 1200 by one emphasizes that in the end, you have the entire whole original amount plus a little bit more. It isn't a big deal. Perhaps you've heard of the Distributive Law of Multiplication over Addition, which comes in a variety of forms, one of which is A*X + B*X = (A+B)*X. This is sometimes called the rule for multiplying out something, or the rule for factoring out something, depending on how you are using it. Here I want to use it to help with factoring out 1200 as follows: (.05 * 1200) + (1 * 1200) = (.05 + 1) * 1200 = 1.05 * 1200 = 60. Without the "one times" in there, you might not notice the connection. The benefit of this is that it shows a calculator shortcut for figuring out the total. Instead of figuring out the increase as a first operation, and then adding in the principal as another operation, you can do the "1 + .05 = 1.05" part in your head, and then multiply the 1200 original amount by 1.05 as the one and only operation. This will not save you enough time to go fishing, but it is important to understand.