If $15,000 is invested at ﻿7 1 half percent sign﻿ for 10 years, find the future value if the interest is compounded monthly. Please round the answer to the nearest cent ( two decimal places ).


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.

If $15,000 is invested at 7 1/2% for 10 years, find the future value if the interest is compounded monthly. Please round the answer to the nearest cent (two decimal places).

Discover how to calculate the future value of $15,000 invested at 7.5% for 10 years with monthly compounding. This detailed solution covers compound interest calculations, including the formula A = P(1 + r/n)^(nt), and rounds the answer to two decimal places.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation