You deposit $1000 in an account that pays 7% interest compounded 
semiannually. After 5 years, the interest rate is increased to 7.08% 
compounded quarterly. Whatwill be the value of the account after a total
 of 10 years? Round to the nearest dollar as needed.

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.

You deposit $1000 in an account that pays 7% interest compounded semiannually. After 5 years, the interest rate is increased to 7.08% compounded quarterly. What will be the value of the account after a total of 10 years? Round to the nearest dollar as needed.

Learn how to calculate the future value of an investment with a principal of $1000, starting with 7% interest compounded semiannually for 5 years, and increasing to 7.08% compounded quarterly for the next 5 years. This example covers compound interest and exponential growth concepts. Ideal for high school students in Grades 10-12.

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