This problem is related to the concept of continuous compounding, which is a method of calculating the interest earned on an account over a certain period of time. The formula for calculating the principal amount for a continuously compounded account earning 3.9% for 15 years is as follows:
P = A/ (1 + r)^t
Where P is the principal, A is the balance after 15 years, r is the rate of interest and t is the number of years.
In this problem, P = $4,768,549.11, A = $2,656,586.66, r = 3.9% and t = 15.
Therefore, the principal for the continuously compounded account earning 3.9% for 15 years is $4,768,549.11