Amy is offred an investment of $20,000 that would pay $70,000 in 20 years.
Calculate the return on the proposed $20,000 investment and indicate the factors entering into your recommendation to accept or reject it.

To evaluate Amy's proposed investment of $20,000, we need to calculate the **annual return** or **rate of return** over the 20-year period. This is often done using the **Compound Annual Growth Rate (CAGR)** formula, which reflects the consistent rate of return per year.

The formula for CAGR is:

\[
\text{CAGR} = \left( \frac{{\text{Final Value}}}{{\text{Initial Value}}} \right)^{\frac{1}{n}} - 1
\]

Where:
- **Final Value** = $70,000 (the value after 20 years),
- **Initial Value** = $20,000 (the initial investment),
- **n** = 20 years (the investment period).

### Step-by-Step Calculation:
1. Substitute the values into the formula:
   \[
   \text{CAGR} = \left( \frac{{70,000}}{{20,000}} \right)^{\frac{1}{20}} - 1
   \]

2. Simplify:
   \[
   \text{CAGR} = \left( 3.5 \right)^{\frac{1}{20}} - 1
   \]

3. Now calculate the value of $ (3.5)^{\frac{1}{20}} $.

Let me calculate this for you.The Compound Annual Growth Rate (CAGR) for Amy's investment is approximately **6.46%** per year.

### Factors to Consider for Accepting or Rejecting the Investment:
1. **Risk Level**: What is the risk associated with this investment compared to alternatives?
2. **Inflation**: Will a 6.46% return outpace inflation over the next 20 years, ensuring real growth in purchasing power?
3. **Market Comparison**: How does this return compare to other typical long-term investments (e.g., stock market, bonds)?
4. **Liquidity**: Can Amy afford to lock away the $20,000 for 20 years, or does she need more liquid investments?
5. **Personal Financial Goals**: Does this investment align with Amy's financial goals and time horizon?

Would you like further details or have any questions?

Here are 5 related questions:
1. How does CAGR differ from simple interest?
2. What are typical stock market returns over a 20-year period?
3. How does inflation impact long-term investments?
4. What types of investments offer higher returns but come with more risk?
5. What role does liquidity play in investment decisions?

**Tip**: Always consider the risk-adjusted return, not just the percentage return, when evaluating investments.

Amy is offered an investment of $20,000 that would pay $70,000 in 20 years. Calculate the return on the proposed $20,000 investment and indicate the factors entering into your recommendation to accept or reject it.

Learn how to calculate the Compound Annual Growth Rate (CAGR) for an investment of $20,000 that grows to $70,000 over 20 years. This problem covers key financial math concepts and is suitable for students in Grades 10-12. Explore factors such as risk, inflation, and market comparison in investment decisions.

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