Live Forever Insurance Company is selling a perpetual annuity contract that pays $2,400 monthly. The contract currently sells for $332,000.

What is the monthly return on this investment vehicle?

Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.

What is the APR?

Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.

What is the effective annual return?

Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.

To solve these problems, we need to use financial formulas related to annuities and returns. Let's break it down step by step.

### 1. **Monthly Return Calculation:**

The formula for the monthly return ($r_{\text{monthly}}$) on an investment is given by the perpetuity formula:

\[
r_{\text{monthly}} = \frac{\text{Monthly Payment}}{\text{Price of the Contract}}
\]

In this case:
- The monthly payment is $ P = 2400 $ dollars.
- The price of the contract is $ C = 332,000 $ dollars.

Substitute these values into the formula:

\[
r_{\text{monthly}} = \frac{2400}{332000}
\]

Let's calculate that.

### 2. **Annual Percentage Rate (APR):**

The Annual Percentage Rate (APR) is the monthly return multiplied by 12 (since there are 12 months in a year):

\[
\text{APR} = r_{\text{monthly}} \times 12
\]

We'll calculate this using the value for $r_{\text{monthly}}$ from the first step.

### 3. **Effective Annual Return:**

The effective annual return (EAR) takes into account the compounding effect over the year. It is calculated as:

\[
\text{EAR} = \left(1 + r_{\text{monthly}}\right)^{12} - 1
\]

Now, let's compute all of these step by step.Here are the results:

1. **Monthly Return**: $0.72\%$
2. **APR (Annual Percentage Rate)**: $8.67\%$
3. **Effective Annual Return (EAR)**: $9.03\%$

Would you like more details or have any further questions? 

Here are five follow-up questions that can expand on this topic:

1. How does compounding affect the difference between APR and EAR?
2. What are some other common types of annuities besides perpetual annuities?
3. How does changing the monthly payment or the contract price affect the return rates?
4. What are the risks and benefits of investing in a perpetual annuity?
5. How would inflation impact the real return on a perpetual annuity?

**Tip:** Always compare both the APR and EAR when evaluating long-term investments, as compounding can significantly impact the effective return.

Live Forever Insurance Company is selling a perpetual annuity contract that pays $2,400 monthly. The contract currently sells for $332,000.

What is the monthly return on this investment vehicle?

What is the APR?

What is the effective annual return?

Learn how to calculate the monthly return, APR, and effective annual return (EAR) for a perpetual annuity contract that pays $2,400 per month and sells for $332,000. Step-by-step breakdowns of the formulas used, including the perpetuity formula and compounding interest. Suitable for finance students and professionals.

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