Answer: It will take about 8.5 years for the balance of the savings account to reach $3827.25.
Explanation:
To find the number of years it will take for the balance of the savings account to reach $3827.25, we can set up the following equation:
$3500 * (1 + 0.011 * t) = 3827.25$
We can then solve for t, the number of years, by dividing both sides of the equation by 3500 and then rearranging the terms to get t by itself:
$t = \frac{3827.25 - 3500}{3500 * 0.011}$
Next, we can plug in the given values and solve for t to find the number of years it will take for the balance of the account to reach $3827.25:
$t = \frac{3827.25 - 3500}{3500 * 0.011} = \frac{327.25}{38.5} = 8.5$
Therefore, it will take about 8.5 years for the balance of the savings account to reach $3827.25.