To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the future value, P is the present value, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, P = $400, r = 2.5%, and we want to find t when A = $800. We can assume that the interest is compounded annually, so n = 1.
Substituting these values into the formula, we get:
$800 = $400(1 + 0.025/1)^(1t)
Simplifying and solving for t, we get:
t = ln(2) / ln(1.025) = 27.36 years
Therefore, it will take about 27.36 years for the premium to increase to $800.