Question

Why 5% is equal to multiplying by 1.05?

Answer 1

multiplying by one makes no difference in the final result. I can think of two possible reasons for doing this. You might refer to "the original amount" or "the whole original amount" depending on whether you wish to give emphasis by adding the extra word. Multiplying 1200 by one emphasizes that in the end, you have the entire whole original amount plus a little bit more. In other words, it's not a big deal. Perhaps you have run across the Distributive Law of multiplication over addition, which has many forms, among 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 You probably would not notice this connection without the "one times" in there. 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 is not going to save you enough hours to take off fishing, but it's not a bad thing to understand.