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I have a very basic understanding of Present Value of a Perpetuity.

Present value = Amount / interest

I have 2 questions below:

(a) Suppose that the annual interest rate is 10%. What is the value of a perpetuity that pays $30 every year from the beginning of next year?

(b) Suppose that the annual interest rate is 5%. What is the value of a perpetuity that pays $100 every other year from the beginning of next year?

According to the formula:

(a) PV = 30 / 0.1 = $300 and
(b) PV = 100 / 0.5 = $200

But the questions have "beginning of next year"? what does this mean? How can I calculate the value of a perpetuity of these 2 questions?

mhoran_psprep
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grooot
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1 Answers1

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Your answer to a) is correct: PV = 30 / 0.1 = $300

"from the beginning of next year" means start with $300, wait a year over which time $30 interest accrues, then withdraw it, starting again at $300.

For b) use a two-year period, so use r = (1 + 0.05)^2 - 1 = 0.1025

However, the first withdrawal should happen after one year,

so adjust the two-year cycle to start with x = PV (1 + 0.05) - 100

Now x = 100/0.1025

and PV = (x + 100)/(1 + 0.05) = 1024.39

Chris Degnen
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