To calculate the accumulated value of the investment, we need to break the problem into two periods: the first 5 years with 3.30% interest compounded semi-annually, and the next 6 years with 5.40% interest compounded semi-annually.

The formula to calculate the accumulated value $A$ for compound interest is:

$A = P \left( 1 + \frac{r}{n} \right)^{nt}$

Where:

• $A$ is the accumulated value
• $P$ is the principal (initial investment)
• $r$ is the annual interest rate (decimal form)
• $n$ is the number of compounding periods per year (since it's compounded semi-annually, $n = 2$)
• $t$ is the time in years

Let’s calculate in steps.

Step 1: Calculate the accumulated value after the first 5 years

For the first 5 years:

• $r = 3.30\% = 0.033$
• $n = 2$ (since it's compounded semi-annually)
• $t = 5$ years

The formula becomes: $A_1 = P \left( 1 + \frac{0.033}{2} \right)^{2 \times 5}$ $A_1 = P \left( 1 + 0.0165 \right)^{10}$ $A_1 = P (1.0165)^{10}$

Step 2: Calculate the accumulated value after the next 6 years with 5.40% interest

After the first 5 years, the new principal is $A_1$, and it earns interest for another 6 years at 5.40% compounded semi-annually.

• $r = 5.40\% = 0.054$
• $n = 2$
• $t = 6$ years

The formula for the next 6 years becomes: $A_2 = A_1 \left( 1 + \frac{0.054}{2} \right)^{2 \times 6}$ $A_2 = A_1 \left( 1 + 0.027 \right)^{12}$ $A_2 = A_1 (1.027)^{12}$

Step 3: Combine both periods

Now, we combine both calculations. The accumulated value at the end of 11 years is:

$A = P (1.0165)^{10} (1.027)^{12}$

You will need to plug in the initial investment amount $P$ to find the final accumulated value.

Let me know if you have a specific principal value, or if you'd like me to proceed further!