To find the future value of an investment compounded monthly, we use the compound interest formula:

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

Where:

• $A$ is the future value of the investment.
• $P$ is the principal amount (initial investment), which is $15,000.
• $r$ is the annual interest rate (as a decimal), which is $7.5\%$ or $0.075$.
• $n$ is the number of times the interest is compounded per year, which is 12 (monthly).
• $t$ is the number of years, which is 10.

Now, plug the values into the formula:

$A = 15000 \left(1 + \frac{0.075}{12}\right)^{12 \times 10}$

First, calculate the monthly interest rate:

$\frac{0.075}{12} = 0.00625$

Next, calculate the total number of compounding periods:

$12 \times 10 = 120$

Now, calculate the future value:

$A = 15000 \left(1 + 0.00625\right)^{120} = 15000 \left(1.00625\right)^{120}$

$A = 15000 \times 2.093443$

$A \approx 31,401.65$

The future value of the investment is approximately $31,401.65.

Would you like more details on any part of this process or have any further questions?

Related Questions:

1. How would the future value change if the interest rate were compounded quarterly?
2. What is the total interest earned over the 10-year period?
3. How would the formula change for continuous compounding?
4. How would the result change if the investment period was 5 years instead of 10?
5. How can you determine the interest rate if you only know the principal, future value, and time?

Tip:

Always ensure the interest rate is in decimal form before plugging it into the compound interest formula.