Question

Given an interest rate of 4.2 percent per year, what is the value at date t = 7 of a perpetual stream of $2,600 payments that begins at date t = 15? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

To find the value of the perpetuity at t= 7, we first need to use the PV of a perpetuity equation. Using this equation we find:

PV = $2,600 / 0.042 = $61,904.76.

Remember that the PV of a perpetuity (and annuity) equations give the PV one period before the first payment, so, this is the value of the perpetuity at t= 14.

To find the value at t = 7, we find the PV of this lump sum as:

$PV = 61,904.76 / 1.042^7 = 46,414.11.$