Answer: 7 years.
Explanation:
We can use the formula for compound interest to solve this problem. The formula is:
A = P(1 + r/n)^(nt)
where A is the ending balance, P is the principal (initial investment), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
We know the principal, P, is $555, the annual interest rate, r, is 12.6%, and the ending balance, A, is $5,600. We also know that the interest is compounded quarterly, so n = 4.
Plugging in these values, we get:
5600 = 555(1 + 0.126/4)^(4t)
Simplifying and solving for t, we get:
t = (1/4) * log(5600/555) / log(1 + 0.126/4) = 7
Therefore, it will take 7 years for the account to reach a balance of $5,600.