Question

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.

Answer 1

To calculate the value of an investment that pays $100 every two years, starting two years from now and continuing indefinitely, we can treat this as a perpetuity.

The cash flow of $100 occurs every two years, so we need to find the present value of these cash flows. Since this is a perpetuity, we will use the formula for the present value of a perpetuity:

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

Where:
- \( PV \) = Present value of the perpetuity
- \( C \) = Cash flow per period
- \( r \) = Effective interest rate per period

First, we need to determine the effective interest rate per two-year period. Given the annual interest rate is 6%, we can calculate the two-year rate as follows:

\[
r = (1 + 0.06)^2 - 1 = 1.1236 - 1 = 0.1236 \text{ or } 12.36\%
\]

Now, we can find the present value of the cash flows of $100 every two years indefinitely:

\[
PV = \frac{C}{r} = \frac{100}{0.1236} \approx 809.66
\]

This value, however, is the present value at the time the cash flows start (which is two years from now). To find the present value today, we must discount this amount back to today using the annual interest rate over two years:

\[
PV_{today} = \frac{809.66}{(1 + 0.06)^2} = \frac{809.66}{1.1236} \approx 720.40
\]

Thus, the present value today of the investment is:

\[
\boxed{720.40}
\]