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 calculate the return on an investment of $20,000 that pays $70,000 in 20 years, we can determine the **annual rate of return** using the formula for compound interest:

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

Where:
- $ A $ = future value of the investment ($70,000)
- $ P $ = initial investment or principal ($20,000)
- $ r $ = annual interest rate (rate of return)
- $ t $ = number of years (20)

We need to solve for $ r $ (the rate of return). Rearranging the formula:

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

Substituting the given values:

\[
r = \left( \frac{70,000}{20,000} \right)^{\frac{1}{20}} - 1
\]

Now, let's calculate this.The annual rate of return on this investment is approximately **6.46%**.

### Factors to consider when making a recommendation:
1. **Inflation Rate**: Compare the return with the expected inflation rate over 20 years. If inflation is high, the real purchasing power of the $70,000 in 20 years might be significantly lower.
2. **Risk Level**: Consider the risk associated with the investment. A return of 6.46% could be attractive for low-risk investments, but not for high-risk ones.
3. **Alternative Investments**: Analyze if other available investments offer a higher return with similar or lower risk.
4. **Liquidity**: Determine if the investment locks in the money for 20 years without easy access to the funds.
5. **Market Conditions**: Assess the economic and market conditions that could affect the investment's growth or potential for loss over time.

### Would you like more details or have any questions?

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**Related Questions:**
1. What is the impact of inflation on the real return of this investment?
2. How does this 6.46% compare to the average stock market return over the past 20 years?
3. What alternative investment opportunities could yield a similar return with lower risk?
4. What is the role of compound interest in long-term investments like this one?
5. How do different risk profiles affect the choice of investments?

**Tip:** Always consider both the nominal return and the real return (after inflation) when evaluating long-term investments.

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.

Discover how to calculate the annual rate of return on a $20,000 investment that grows to $70,000 over 20 years using compound interest. This solution explains key financial concepts and formulas, ideal for college-level finance or economics students.

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