The balance after 4 years if the interest is compounded continuously can be calculated using the formula for continuous compounding:
A = Pe^rt
where A is the balance after the period, P is the initial principal, r is the interest rate, and t is the time in years.
In this case, the initial principal is $12,000, the interest rate is 3%, and the time is 4 years.
A = 12000 * e^(0.03*4)
A = 12000 * e^0.12
A = 12000 * 1.128037
A = $13,529.96