To calculate the maturity value of an investment, we use the compound interest formula:

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

Where:

• $A$ is the maturity value (the amount after interest),
• $P$ is the principal (the 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 in years.

Given:

• $P = 6100$ (the initial investment),
• $r = 4\% = 0.04$,
• $n = 2$ (since the interest is compounded semiannually),
• $t = 8$ years.

Now, substitute the values into the formula:

$A = 6100 \left( 1 + \frac{0.04}{2} \right)^{2 \times 8}$

Simplifying inside the parentheses:

$A = 6100 \left( 1 + 0.02 \right)^{16}$ $A = 6100 \times \left( 1.02 \right)^{16}$

Now calculate $1.02^{16}$:

$1.02^{16} \approx 1.3728$

Multiply by the principal:

$A \approx 6100 \times 1.3728 \approx 8365.08$

Thus, the maturity value of the investment is approximately $8365.08.

---

Would you like a more detailed breakdown or further clarification?

Related Questions:

1. How would the maturity value change if the interest were compounded annually instead of semiannually?
2. What is the formula for calculating compound interest for different compounding periods?
3. How do I calculate compound interest when interest is compounded quarterly?
4. What is the difference between simple and compound interest calculations?
5. How would the maturity value change if the interest rate were increased to 5%?

Tip: When calculating compound interest, ensure that the rate is adjusted for the compounding frequency (e.g., for semiannual compounding, divide the annual rate by 2).