Question 8
Assume the annual interest rate is 6%. Calculate the value of an investment that pays $100 every two years, starting two years from now and continuing forever.

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.

To calculate the value of an investment that pays $100 every two years indefinitely (perpetuity), we can use the formula for the present value of a perpetuity with payments made at intervals. The formula is:

\[
PV = \frac{P}{r}
\]

However, since the payments are made every two years instead of every year, we need to adjust the interest rate accordingly. Let's proceed step by step.

### Step 1: Adjust the Interest Rate
Given:
- Annual interest rate $ r = 0.06 $ (6%)
- Payments are made every two years.

The effective interest rate for every two years (which we'll use as our discount rate) is:

\[
r_{\text{effective}} = (1 + r_{\text{annual}})^2 - 1
\]

But for simplicity, since the payment is every two years, the effective interest rate can also be taken as $ r_{\text{biennial}} = 2 \times r_{\text{annual}} = 2 \times 0.06 = 0.12 $ (12% every two years).

### Step 2: Calculate the Present Value (PV)
The present value (PV) of a perpetuity where payments are made every two years is:

\[
PV = \frac{P}{r_{\text{biennial}}}
\]

Where:
- $ P = 100 $ (payment every two years)
- $ r_{\text{biennial}} = 0.12 $

\[
PV = \frac{100}{0.12} = 833.33
\]

### Final Answer:
The value of the investment is **833.33**.

Would you like more details on the steps? Here are some related questions for further exploration:

1. How would the value change if the interest rate were compounded semi-annually?
2. What if the payments were made every year instead of every two years?
3. How would the investment's value be affected if the payment amount increased by a fixed percentage each period?
4. Can you calculate the future value of this investment at a specific point in time?
5. What is the difference in investment value when considering simple versus compound interest?

**Tip:** Always adjust the interest rate to match the payment interval when dealing with perpetuities or annuities.

Learn how to calculate the present value of an investment that pays $100 every two years indefinitely with a 6% annual interest rate. This problem covers financial mathematics concepts, including perpetuity calculations and effective interest rates.

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