The problem asks for the accumulated value of an investment of $10,000 for 7 years at an interest rate of 1.35%, compounded semiannually. To solve this, we can use the formula for compound interest:

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

Where:

• $A$ is the accumulated value (what we're solving for),
• $P = 10,000$ is the initial investment (principal),
• $r = 0.0135$ is the annual interest rate (1.35% as a decimal),
• $n = 2$ is the number of times the interest is compounded per year (semiannually means twice per year),
• $t = 7$ is the number of years.

Now, plugging the values into the formula:

$A = 10,000 \left(1 + \frac{0.0135}{2}\right)^{2 \times 7}$

Let me calculate the result for you.The accumulated value of the investment, compounded semiannually, is approximately $10,987.60.

Would you like further details or have any questions?

Here are five related questions to expand on this concept:

1. How does the accumulated value change if the investment is compounded quarterly?
2. What is the accumulated value if the interest is compounded monthly?
3. How would the formula change if the interest were compounded continuously?
4. What would the accumulated value be for different principal amounts, like $15,000 or $20,000?
5. How does the term of the investment (number of years) affect the accumulated value?

Tip: When solving compound interest problems, always convert the percentage interest rate into a decimal form (e.g., 1.35% becomes 0.0135) before applying it in the formula.