Life Income Fund: formula for Ontario LIFs

The prescription for calculating the Maximum Annual Withdrawals for a LIF is as follows:
  • For fifteen years from the date when the LIF began, one computes the present value of a $1.00 annual payment, using an annual rate:
    Maximum of CANSIM and 6.0%.
  • Thereafter, until age 90, compute the present value using 6.0% and add this to the above giving a number we'll call PV.
  • The Maximum Annual LIF Withdrawal is a percentage of the LIF Balance as of January 1, that percentage being 1/PV.

  1. A = The age when you began the LIF withdrawals.
  2. T = your current age.
  3. J = 0.060 ... meaning 6.0%
  4. K = Canadian Government long bond rate (CANSIM Rate) ... if it's 5.67%, put K = 0.0567
  5. I = Maximum of J and K ... we're calling this the MAX Rate
  6. x = 1/(1+I)
  7. y = 1/(1+J)
  8. Calculate the Present Value of an annual payment of $1.00 at the rate I, from your current age T to age A+15, namely
    P = 1 + x + x2 + ... + xA+14-T = (1-xA+15-T)/(1-x)
  9. Calculate the Present Value, at age A+15, of an annual payment of $1.00 at the rate J, to age 90, namely
    1 + y + y2 + ... + y90-(A+15) = (1-y75-A)/(1-y) the Value of umpteen $1.00 payments, at age A+15
    and, bringing it to the present (A+15-T years earlier than at A+15 ... to your present age), gives:
    Q = x(A+15-T) (1-y75-A)/(1-y)
  10. PV = P + Q
Uh ... one other thing:
If you're over 75 years old then 15 years at the MAX Rate will take y'all over 90, so don't bother with the MAX Rate; use the 6.0% until age 90.

Here's a picture of the LIF Maxima (as well as RRIF/LIF Minima):

Here's a Spreadsheet formula:
PV = IF(T<=A+14,(1-x^(A+15-T))/(1-x)+x^(A+15-T)*(1-y^(75-A)/(1-y),(1-y^(90-T))/(1-y))

... OR, of you just want a spreadsheet which looks like this:

then to download

If'n you'd like just a number, play with this calculator:

Your Age (on Jan 1) =     CANSIM long bond rate = %     Jan 1 LIF balance = $
Maximum Annual LIF Income = %   x (January 1 balance)

    I'm pretty sure this gives the correct prescription for calculating the LIF Maximum, but you should check out: LIF Maxima Tables