If an initial investment of $2,800 grows to $35,000 in 18 years, what annual interest rate (as a %) compounded annually did this investment earn? (Round your answer to two decimal places.)
  %


To determine the annual interest rate for this investment compounded annually, we can use the formula for compound interest:

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

Where:
- $ A $ is the final amount ($35,000),
- $ P $ is the initial principal ($2,800),
- $ r $ is the annual interest rate (which we need to find),
- $ t $ is the time in years (18 years).

Rearranging the formula to solve for $ r $:

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

Now, let's plug in the values:

\[
r = \left( \frac{35,000}{2,800} \right)^{\frac{1}{18}} - 1
\]

I'll calculate this now.The annual interest rate, compounded annually, is approximately **15.06%**.

Would you like further details on this calculation or have any other questions?

Here are 5 related questions to deepen your understanding:
1. How does the time period affect the growth of an investment with compound interest?
2. What is the difference between simple and compound interest?
3. How would the annual interest rate change if the investment period were shorter, say 10 years?
4. What is continuous compounding, and how does it differ from annual compounding?
5. How can you calculate the future value of an investment with monthly compounding?

**Tip:** Always remember, the frequency of compounding can significantly impact the growth of an investment over time!

If an initial investment of $2,800 grows to $35,000 in 18 years, what annual interest rate (as a %) compounded annually did this investment earn? (Round your answer to two decimal places.)

Learn how to calculate the annual interest rate for an investment that grows from $2,800 to $35,000 over 18 years using the compound interest formula. Detailed solution with step-by-step calculation, suitable for advanced algebra students. Final result: 15.06%.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation