Supplementary Information: The 20-year Rule

A perpetuity is an annuity whose periodic payments (PMT) continue forever, based on an original endowment (PV) and a constant compound interest rate.

Solving Perpetuities with Formulas

The present value of a simple ordinary perpetuity is PV= \frac{PMT}{i}

 

Calculating the present value of a general perpetuity requires two additional formulas:
  • i_2 = (1+i)^c-1
  • c =  \frac{C/Y}{P/Y}, where C/Y = # compoundings per year, P/Y= # of payments per year
A perpetuity due requires a fourth formula.
  • Can it be done using the financial calculator?
  • How do you enter an infinite number of payments?
N must be large enough to reflect a perpetuity, but not too large for the calculator to handle (in some cases)!

We use the following rule:

The present value of any perpetuity is identical to
the present value of an equivalent annuity, whose
term is 20 years divided by the perpetuity’s nominal interest rate (as a decimal fraction)

i.e.

  • Number of years= \frac{20}{j}
  • N= \frac{20}{j} *P/Y

NOTE:

  • N Should be rounded up if not an integer
  • This is the minimum number of payments required to represent a perpetuity
  • Larger values are fine, but sometimes only up to a certain point

See the attached Excel Template on using the 20 year rule: Perpetuities using 20 year rule

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Using Excel in Business Math Copyright © by Lisa Koster is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

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