Find the principal P that will generate the given future value​ A, where A=​$12,000 at 6​% compounded annually for 10 years.

The principal P will be approximately ​$ round to 2 decimal places as need

To find the principal $ P $ that will generate a future value $ A $ of $12,000 at an annual interest rate of 6% compounded annually for 10 years, we use the formula for compound interest:

\[ A = P(1 + r)^n \]

where:
- $ A $ is the future value ($12,000)
- $ P $ is the principal
- $ r $ is the annual interest rate (0.06)
- $ n $ is the number of years (10)

Rearranging the formula to solve for $ P $:

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

Substitute the given values:

\[ P = \frac{12000}{(1 + 0.06)^{10}} \]

Calculate the value:

\[ P = \frac{12000}{(1.06)^{10}} \]

First, calculate $ (1.06)^{10} $:

\[ (1.06)^{10} \approx 1.790847 \]

Now, divide $12,000 by this value:

\[ P \approx \frac{12000}{1.790847} \approx 6701.38 \]

Therefore, the principal $ P $ will be approximately $6,701.38.

Would you like more details or have any questions?

Here are 8 relative questions to expand your understanding:

1. What is the formula for calculating compound interest?
2. How does the compounding frequency affect the future value of an investment?
3. What would be the future value if the principal was $6,701.38 at 6% interest compounded annually for 10 years?
4. How does the interest rate impact the principal needed to achieve a specific future value?
5. What would the principal be if the interest rate was 5% instead of 6%?
6. How does the duration of the investment affect the required principal?
7. What is the difference between compound interest and simple interest?
8. How can the compound interest formula be applied to monthly or quarterly compounding periods?

**Tip:** When dealing with financial calculations, it's essential to understand the impact of different compounding periods on the growth of investments.

Learn how to calculate the principal P that will yield a future value A of $12,000 at an annual interest rate of 6% compounded annually over 10 years. Step-by-step solution using compound interest formula. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation