To find the accumulated value of an investment with compounded interest, we will use the compound interest formula:

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

Where:

• $A$ is the accumulated value (final amount)
• $P$ is the principal amount (initial investment)
• $r$ is the annual interest rate (as a decimal)
• $n$ is the number of times the interest is compounded per year
• $t$ is the time the money is invested for, in years

Given data:

• Principal, $P = 25,000$
• Interest rate, $r = 1.35\% = 0.0135$
• Time, $t = 7$ years
• Compounding frequency: semiannually, which means $n = 2$

Semiannual Compounding:

Substituting the known values into the formula:

$A = 25,000 \left(1 + \frac{0.0135}{2}\right)^{2 \times 7}$ $A = 25,000 \left(1 + 0.00675\right)^{14}$ $A = 25,000 \left(1.00675\right)^{14}$

Now, let's calculate $A$.

$A = 25,000 \times 1.10095$ $A = 27,523.72$

So, the accumulated value of the investment, compounded semiannually, is $27,523.72.

Would you like me to calculate the values for the other compounding frequencies as well? Or do you have any questions on the steps used?

Here are some related questions you may find interesting:

1. How does the number of compounding periods per year affect the accumulated value?
2. How does the interest rate impact the final amount of an investment?
3. What would happen if the investment was compounded annually instead of semiannually?
4. How do you convert an annual interest rate into a decimal for calculations?
5. What are the advantages of continuous compounding compared to other methods?

Tip: Always remember to convert the percentage to a decimal before using it in the formula!