It will a little over a week. Except for one your tamagotchi is born, one human day is equal to one tamagotchi year of life. Your tamagotchi will become an adult at roughly 5 years of age, give or take. Once he/she is an adult you will either mate with another tamagotchi or get the matchmaker a few days later and the process begins again.
And it goes faster if you don't pause it. If you don't have your tama in school, put it to sleep when you leave for school and that way it still gets older. :]