How is the present value (PV) of a perpetuity calculated?

The present value (PV) of a perpetuity is calculated using the formula PV = PMT/i. In this formula, PMT represents the cash payment received or paid in each period, and i denotes the interest rate or discount rate.

This formula is derived from the concept that a perpetuity is a stream of cash flows that continues indefinitely. To determine how much this stream is worth today, we use the concept of present value. By dividing the payment amount by the interest rate, we find the present value of an infinite series of cash flows that are discounted back to the present at the specified interest rate.

For example, if a perpetuity pays $100 annually and the interest rate is 5% (or 0.05), the present value would be calculated as follows: PV = $100 / 0.05, which results in a present value of $2,000. This reflects the value today of receiving $100 every year forever, discounted at the rate of 5%.

The other calculations mentioned in the alternative options do not accurately represent the relationship between cash flows, interest rates, and present value in the context of perpetuities.