To find the balance of the account after 3 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where A is the final amount, P is the initial principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, the initial principal is $2,600, the interest rate is 4.2% (expressed as a decimal), the number of times the interest is compounded per year is 12 (monthly), and the number of years is 3.
So, we can plug these values into the formula:
A = 2600(1 + 0.042/12)^(12*3)
A = 2600(1.0035)^36
A = 2600 * 3.876
A = 10,049.6
The balance of the account after 3 years is $10,049.6.