Elaine received $$120,000$ as a gift on New Year's Day $($January $1)$ in the past, and she put the money into a bank account that same day. It is now New Year's Day less than $7$ years later, and she has $$168,306\mathrm{.}21$ in the account. This bank account pays $7\%$ per year, and she has not added or taken out money since the initial deposit. How many years ago did she receive this gift? Give your answer as an integer $($the number of years$).$ Elaine received this gift