Can you help with a math question about compound interest?

For whatever reason my brain is not functioning on all eight cylinders.

Here is the question: If you have a sum of money, let’s say $100,000, and you have the interest go into a separate account that earns the same interest as the original account, will you have the same amount of total money at the end of five years with two accounts as if you kept all of the money in the original account?