What is the future value of $6000 earning 12% interest, compounded monthly, for 6 years? (Round your answer to two decimal places.)

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

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

Where:
- $ FV $ is the future value.
- $ PV $ is the present value (initial amount).
- $ r $ is the annual interest rate (decimal).
- $ n $ is the number of times interest is compounded per year.
- $ t $ is the time the money is invested for, in years.

For this problem:
- $ PV = \$6,000 $
- $ r = 12\% = 0.12 $
- $ n = 12 $ (since interest is compounded monthly)
- $ t = 6 $ years

Now, let's plug these values into the formula:

\[ FV = 6000 \left(1 + \frac{0.12}{12}\right)^{12 \times 6} \]

First, calculate the monthly interest rate:

\[ \frac{0.12}{12} = 0.01 \]

Next, calculate the total number of compounding periods:

\[ 12 \times 6 = 72 \]

Now calculate the expression inside the parentheses:

\[ 1 + 0.01 = 1.01 \]

Raise this to the power of 72:

\[ 1.01^{72} \approx 2.012196 \]

Finally, multiply by the initial amount:

\[ FV = 6000 \times 2.012196 \approx 12073.18 \]

So, the future value of $6,000 earning 12% interest compounded monthly for 6 years is approximately **$12,073.18**.

Do you want any more details or have any questions?

Here are some related questions:

1. What is the difference between compound interest and simple interest?
2. How does changing the compounding frequency to quarterly affect the future value?
3. What is the future value of $6,000 earning 12% interest compounded quarterly for 6 years?
4. How can you calculate the present value if you know the future value and the interest rate?
5. What is the impact of increasing the investment period to 10 years?
6. How does the future value change with a different interest rate, for example, 10%?
7. What would be the future value if the initial investment was $8,000 instead of $6,000?
8. What is the effective annual rate (EAR) for an interest rate of 12% compounded monthly?

**Tip:** When dealing with compound interest, always ensure that the rate and the number of compounding periods are aligned. For monthly compounding, use the monthly interest rate and the total number of months.

Learn how to calculate the future value of $6,000 earning 12% interest compounded monthly for 6 years. Understand the compound interest formula and step-by-step calculation with a detailed explanation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation