What is the principal that will grow to $\$ 3500$ in three years, two months at $8 \%$ compounded semi-annually? The principal is $\$$ (Round to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Step 1 ：We are given that the amount of money accumulated after a certain period of time (A) is $3500, the annual interest rate (r) is 8% or 0.08 in decimal form, the number of times that interest is compounded per year (n) is 2 (since it's compounded semi-annually), and the time the money is invested for (t) is 3 years and 2 months or approximately 3.16667 years.

Step 2 ：We can use the formula for compound interest, which is \(A = P(1 + r/n)^{nt}\), where P is the principal amount (the initial amount of money).

Step 3 ：We can rearrange this formula to solve for P: \(P = A / (1 + r/n)^{nt}\).

Step 4 ：Substituting the given values into the formula, we get \(P = 3500 / (1 + 0.08/2)^{2*3.16667}\).

Step 5 ：Solving this equation gives us \(P \approx 2730.17\).

Step 6 ：Thus, the principal that will grow to $3500 in three years, two months at 8% compounded semi-annually is approximately \(\boxed{2730.17}\).