To calculate the future value of the account, we need to split the problem into two parts:

1. First 5 years: The account earns 7% interest compounded semiannually.
2. Last 5 years: The interest rate changes to 7.08% compounded quarterly.

Step 1: Future Value After 5 Years at 7% Compounded Semiannually

The formula for compound interest is:

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

Where:

• $A$ is the future value of the investment/loan, including interest.
• $P$ is the principal investment amount ($1000).
• $r$ is the annual interest rate (decimal form).
• $n$ is the number of times that interest is compounded per year.
• $t$ is the time the money is invested for in years.

For the first 5 years:

• $P = 1000$
• $r = 0.07$ (7%)
• $n = 2$ (semiannual compounding)
• $t = 5$ years

Now we can calculate the amount after 5 years:

$A_1 = 1000 \left(1 + \frac{0.07}{2}\right)^{2 \times 5}$

Step 2: Future Value for the Next 5 Years at 7.08% Compounded Quarterly

After 5 years, the interest rate changes to 7.08%, compounded quarterly.

Using the same formula, but this time for the next 5 years:

• The new principal will be the amount from Step 1 ($A_1$).
• The interest rate $r = 0.0708$ (7.08%).
• $n = 4$ (quarterly compounding).
• $t = 5$ years.

We will calculate the future value based on the amount after the first 5 years.

Let me calculate both steps now.