Question

Your aunt, in her will, left you the sum of $5,000 a year forever with payments starting immediately. However, the news is better. She has specified that the amount should grow at 5% per year to maintain purchasing power. Given an interest rate of 12%, what is the PV of the inheritance?

Answer 1

To calculate the present value of an inheritance that is $5,000 a year forever with a growth rate of 5%, given an interest rate of 12%, one must use the formula for the present value of a growing perpetuity. The calculated PV in this scenario is $71,428.57.

Step-by-step explanation:

The question pertains to calculating the present value (PV) of a perpetuity that grows at a constant rate, which is also known as a growing perpetuity. The present value can be calculated using the formula:

PV = C / (r - g)

where C is the initial cash flow ($5,000), r is the discount rate (12% or 0.12 in decimal form), and g is the growth rate of the annuity (5% or 0.05 in decimal form). Inserting these values into the formula gives:

PV = 5,000 / (0.12 - 0.05) = 5,000 / 0.07 = $71,428.57

Therefore, the present value of the inheritance that grows at 5% per year, given a 12% interest rate, is $71,428.57.