To calculate the interest earned on a compound interest investment, we use the formula:

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

where:

• $A$ is the future value of the investment,
• $P$ is the principal (initial amount) of the 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 number of years.

Given:

• $P = 6400$
• $r = 0.11$ (or 11%)
• $n = 12$ (compounded monthly)
• $t = 2$ years

Let's substitute these values into the formula:

$A = 6400 \left(1 + \frac{0.11}{12}\right)^{12 \times 2}$

Calculating this:

1. First, calculate the monthly rate: $\frac{0.11}{12} \approx 0.0091667$

2. Next, add 1 to this rate: $1 + 0.0091667 \approx 1.0091667$

3. Then, raise this to the power of $12 \times 2 = 24$: $1.0091667^{24} \approx 1.23581$

4. Finally, multiply by the principal $P$: $A \approx 6400 \times 1.23581 = 7909.18$

The interest earned is the difference between the future value $A$ and the principal $P$:

$\text{Interest} = 7909.18 - 6400 = 1509.18$

Answer: The interest earned will be approximately $1509.18.

Would you like additional details on the calculation?

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Here are some related questions:

1. What would the interest be if compounded quarterly instead of monthly?
2. How much would be earned over 5 years with the same rate and compounding?
3. What would be the interest with simple interest rather than compound interest?
4. How would the interest differ if compounded daily?
5. What is the formula for compound interest if compounded continuously?

Tip: When working with compound interest, ensure the rate and compounding frequency align with the investment's term for accurate calculations.