A certain savings account offers an annual interest rate of 5%. The interest is compounded yearly. If you initially deposit $1,000, how much will be in the account after 3 years? (Use the formula for compound interest: \( A = P(1 + \frac{r}{n})^{nt} \), where \( A \) is the amount of money accumulated after n years, including interest. \( P \) is the principal amount (the initial amount of money), \( r \) is the annual interest rate (decimal), \( n \) is the number of times that interest is compounded per year, and \( t \) is the number of years the money is invested or borrowed for.) Let's think step by step and output the final answer within \boxed{}.
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