High School
SAT
ACT
University
MCAT
LSAT
DAT
Wize University Introduction to Finance Textbook > Time Value of Money

Perpetuities

AnnuitiesPrevious Section
Growing AnnuitiesNext Section
Popular Courses
Find My Course
0:00 / 0:00

Perpetuities

Perpetuities are simply annuities that never end. All other characteristics of annuities are also characteristics of perpetuities.
  • Perpetuities have indefinite lives, there is no value for n or FV
  • Payments can be at the end of the period (ordinary perpetuities) or at the beginning of the period (perpetuity-due)


Present Value of Ordinary Perpetuity

Present Value of Perpetuity-Due





0:00 / 0:00

Example: Perpetuities

Assume you expect to receive $100 per year forever starting from today. If the appropriate discount rate is 6%. What is the present value of these cash flows?

Practice: Perpetuities

Steve just won a lottery that will pay him $1,000 per month forever, starting in one month. He is considering selling his winning ticket but needs your help in deciding how much he should sell it for. Assuming the appropriate discount rate is 10% compounded semi-annually, what is the minimum he should accept to sell his ticket?

Round the effective rate to at least 6 decimal places and your final answer to the nearest dollar.
Extra Practice
An insurance company is offering depositors a perpetual cash flow if they deposit $1,000,000 today. At a discount rate of 7%, how much of an annual cash flow can the insurance company pay the investor?
With interest at 9% compounded monthly, how much money is required today to provide perpetual income of $14,352.46 per year?
Round your work discount rate to at least 6 decimal places. Round final answer to 2 decimal places.
With interest at 8% compounded annually, how much money is required today to provide perpetual income of $14,316 per year?
What is the PV of a perpetuity of $100 at an interest rate of 6%?
You are offered the right to receive $6,000 per year forever, starting in one year. If your discount rate is 7%, what is this offer worth to you?
An investment will pay you $600 per month starting today, what is the present value using an effective daily rate of 0.1%.
Round your discount rate to at least 6 decimal places.
You have just won a lottery that will pay you $1,000 per week forever starting today. Using a discount rate of 8% compounded monthly, what is the minimum lump sum payment you should accept in exchange for your winning ticket?
Round your discount rate to at least 6 decimal places.
You have just won a lottery that will pay you $1,000 per week forever starting one week from today. Using a discount rate of 8% compounded monthly, what is the minimum lump sum payment you should accept in exchange for your winning ticket?
Round your discount rate to at least 6 decimal places.
An investment you made will begin paying you $1,000 per year forever, starting in one year. If your discount rate is 10% per year, what is the present value of your investment?
Atlas just won a lottery and has been offered two prizes, he must choose one.
Option 1: Take a lump sum of $4,000,000 today.
Option 2: Receive $450,000 per year forever.
You have just purchased a stock that will pay you dividends of $1.60 per month forever starting one month from today. If your expected return is 7% compounded annually, how much did you pay for the stock? Round your final answer to 2 decimal places.
An investment is valued at $821.94 today and promises to make annual payments at the end of each year forever. If the discount rate is 9.8% per year, how much will this investment pay each year? Round your final answer to 2 decimal places.
An investment promises to pay $100 at the end of each year forever. If the discount rate is 6% what is the present value? Round final answer to 2 decimal places.