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Wize University Introduction to Finance Textbook > Time Value of Money

Growing Perpetuities

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Growing Perpetuities

Perpetuities where the recurring payments/cash flows grow at a constant rate (g) each period in perpetuity. Again, because the payments grow each period, the dollar value of the payments is not equal.

Growing perpetuities have the following characteristics:
  • Constant growth rate (g) each period in perpetuity;
  • Regular time interval of payout; and
  • No end date. Continues forever



Watch Out!
In a growing perpetuity, the discount rate (r) must be greater than the growth rate (g).

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Example: Growing Perpetuity

Diane plans to make a donation each year to her favourite charity. One year from today, she wishes to make the first donation of $1,000 and plans to increase her donations by 5% per year. How much should she deposit today so that there will always be money available for her donations if her account earns 8% compounded semi-annually (twice per year)?

Practice: Growing Perpetuities

In two years you will receive $600 from an investment. Every two years after that, your return will increase by 8%. What is the present value of your investment using a rate of 10% compounded monthly?
Extra Practice
An investment will pay you $500 today and 5% more each quarter forever. What is the present value of this investment if your opportunity cost is 25% compounded monthly.
Round your work to at least 6 decimal places and final answers to 2 decimal places.
What is the present value of an investment that will pay you $500 in one year, and 5% more each year indefinitely. The appropriate discount rate is 17% compounded daily.
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 at the end of the year and 5% more per year forever.
An investment will pay you $500 today and 8% more each year. What is the value of this investment if your discount rate is 12%?
An investment will pay you $500 today and 8% more per year indefinitely. At a discount rate of 12%, what is the present value of this investment?
An investment will pay you $500 in one year and 8% more per year indefinitely. At a discount rate of 12%, what is the present value of this investment?