How much interest does a $6715 investment earn at 15% compounded semiannually over six years?

To determine the amount of interest earned on a $6715 investment at 15% compounded semiannually over six years, we use the formula for compound interest:

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

where:
- $ A $ is the future value of the investment/loan, including interest.
- $ P $ is the principal investment amount ($6715).
- $ r $ is the annual interest rate (decimal) (15% or 0.15).
- $ n $ is the number of times that interest is compounded per year (2 for semiannual).
- $ t $ is the time the money is invested for in years (6 years).

Plugging the values into the formula:

\[ A = 6715 \left(1 + \frac{0.15}{2}\right)^{2 \cdot 6} \]

First, calculate the semiannual interest rate:

\[ \frac{0.15}{2} = 0.075 \]

Then calculate the number of compounding periods:

\[ 2 \cdot 6 = 12 \]

Now, substitute these values back into the formula:

\[ A = 6715 \left(1 + 0.075\right)^{12} \]
\[ A = 6715 \left(1.075\right)^{12} \]

Calculate $ (1.075)^{12} $:

\[ (1.075)^{12} \approx 2.404 \]

Now multiply this by the principal:

\[ A \approx 6715 \times 2.404 \]
\[ A \approx 16138.46 \]

To find the interest earned, subtract the principal from the amount:

\[ \text{Interest} = A - P \]
\[ \text{Interest} = 16138.46 - 6715 \]
\[ \text{Interest} \approx 9423.46 \]

So, the interest earned on a $6715 investment at 15% compounded semiannually over six years is approximately $9423.46.

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. How does the interest calculation change if it's compounded quarterly?
2. What would the future value be if the interest rate was 10% instead of 15%?
3. How do you calculate simple interest, and how does it compare to compound interest?
4. What would the interest be if the investment period was 10 years instead of 6 years?
5. How does the frequency of compounding affect the amount of interest earned?
6. What is the formula for continuous compounding, and how does it apply here?
7. How do you convert an annual interest rate to a monthly interest rate for compounding purposes?
8. What impact does a higher principal amount have on the total interest earned over the same period?

**Tip:** Always double-check the number of compounding periods and ensure you correctly convert the interest rate to match the compounding frequency.

Learn how to calculate the interest earned on a $6715 investment at 15% compounded semiannually over six years. Detailed step-by-step solution using compound interest formula. Suitable for financial calculations and educational purposes.

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