A perpetuity will pay $1000 per year,starting five years after the perpetuity is purchased.What is the present value (PV)of this perpetuity on the date that it is purchased,given that the interest rate is 4%?

Question

Quizplus · Accepted Answer

We can calculate the present value of the perpetuity using the formula PV = C/r, where PV is the present value, C is the yearly cash flow and r is the interest rate. Plugging in the numbers, we get PV = 1000/0.04 = $25,000. However, since the payments start 5 years after the perpetuity is purchased, we need to discount the present value by 1/(1+0.04)^5 = 0.8227. Thus, the present value is PV = $25,000 x 0.8227 = $20,547.95, which is closest to answer choice C, $20,548.

A Perpetuity Will Pay $1000 Per Year,starting Five Years After