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.