Question

Consider a perpetuity that pays $110 per year, and the current interest rate is 7.6 percent. Explore the impact on the value of the perpetuity if interest rates were to increase to 9.1 percent. Formulate a comprehensive question guiding respondents through the analysis of the perpetuity's value change.

Answer 1

The value of a perpetuity decreases when interest rates increase, because future payments are discounted at a higher rate, making them less valuable in present terms. A perpetuity paying $110 annually is originally valued at approximately $1447.37 at 7.6% interest but drops to approximately $1208.79 at 9.1% interest.

Step-by-step explanation:

When analyzing the impact of changes in interest rates on the value of a perpetuity, it is important to understand how the present value of future payments is affected. A perpetuity that pays $110 per year at an initial interest rate of 7.6% will have its value calculated as follows:

Value = Payment / Interest Rate.

Hence, the initial value is $110 / 0.076, which equals approximately $1447.37.

If the interest rate increases to 9.1%, the new value of the perpetuity is $110 / 0.091, resulting in approximately $1208.79. This example demonstrates that the value of the perpetuity decreases as the interest rate rises because the same amount of payment in the future is less valuable when discounted by a higher rate. Even though future dollar payments remain the same, the investment's value falls.