Juan invested $24,000 in a mutual fund 3 yr ago. Today his investment is worth $32,735. Find the effective annual rate of return on his investment over the 3-yr period.

To find the effective annual rate of return on Juan's investment, we use the formula for compound interest growth:

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

Where:
- $ A $ is the final amount (\$32,735),
- $ P $ is the initial investment (\$24,000),
- $ r $ is the annual rate of return (what we want to find),
- $ t $ is the time period in years (3 years).

First, we plug the known values into the formula:

\[
32,735 = 24,000(1 + r)^3
\]

### Step 1: Isolate $ (1 + r) $

\[
\frac{32,735}{24,000} = (1 + r)^3
\]

\[
1.36479 = (1 + r)^3
\]

### Step 2: Solve for $ 1 + r $ by taking the cube root

\[
1 + r = \sqrt[3]{1.36479}
\]

### Step 3: Calculate the cube root

\[
1 + r \approx 1.1079
\]

### Step 4: Solve for $ r $

\[
r = 1.1079 - 1
\]

\[
r \approx 0.1079
\]

Thus, the effective annual rate of return is approximately 10.79%.

Let me know if you'd like further details on this, or have any questions! Here are some related questions you can explore:

1. How would the rate change if the investment was for 5 years instead of 3?
2. What would the future value be if the initial investment was $30,000 instead?
3. How does effective annual rate differ from nominal rate in compounding interest?
4. What would the rate be if the final amount was $40,000 instead of $32,735?
5. How is continuous compounding different from annual compounding?

**Tip:** When working with growth formulas, it's important to distinguish between compounding annually, quarterly, or continuously, as it impacts the rate significantly.

Juan invested $24,000 in a mutual fund 3 years ago. Today his investment is worth $32,735. Find the effective annual rate of return on his investment over the 3-year period.

Discover how to calculate the effective annual rate of return for a $24,000 investment that grows to $32,735 over a 3-year period. This problem involves exponential growth and the compound interest formula, ideal for 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