What annual rate of change would make 2,000 grow to 25,000 in 10 years? Note: Please make sure your final answer(s) are in percentage form and are accurate to 2 decimal places. For example 34.56%

We can solve this problem using the formula for compound growth:

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

Where:
- \(A\) is the final amount (25,000),
- \(P\) is the initial amount (2,000),
- \(r\) is the annual growth rate (what we're solving for),
- \(t\) is the number of years (10).

Rearranging the formula to solve for \(r\):

\[
r = \left( \frac{A}{P} \right)^{\frac{1}{t}} - 1
\]

Let's plug in the values and solve for \(r\):

\[
r = \left( \frac{25000}{2000} \right)^{\frac{1}{10}} - 1
\]

Now, I will calculate the value.The annual rate of change that would make 2,000 grow to 25,000 in 10 years is **28.73%**.

Would you like further details on the calculation, or do you have any questions?

Here are 5 related questions for practice:
1. What would the rate be if the growth period were 15 years instead of 10?
2. How much would 2,000 grow to in 5 years with a 28.73% growth rate?
3. What is the formula to calculate the future value of an investment with continuous compounding?
4. If the rate were 25%, what would be the final amount after 10 years?
5. How does the concept of compounding differ from simple interest?

**Tip**: Compound interest grows your investment at an accelerating rate because it earns interest not only on the original amount but also on previously earned interest.

Find the annual growth rate needed for an amount of 2,000 to grow to 25,000 over 10 years using the compound interest formula. Learn the steps involved in solving for the rate with detailed explanations and practice problems. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation