IFR - Lifetime Income Illustrations

Good Morning - 

Could someone please provide me with the actuarial formula (possibly by way of example with the answer) for calculating lifetime income out of the new DOL Interim Final Rule?  I understand generally the assumptions used (age, balance, interest rate and mortality), but my numbers seem way off.  

Thanks!

How "Way off"?  I generated an APR table that gets numbers like Life only = $ 693 and  J&S 100 = $565 @ age 67.  Got the qx from 2008 Applicable Mortality Table.  Certainly not close enough for the actuary but maybe for illustration purposes.

Thank you.  I am factoring in something incorrectly, because I am not close.  

I can also get close.  My calculation using the DOL's assumptions gets me to $640 (not the DOL's $645) based on a balance of $125,000, an interest rate of 1.83%, and a life expectancy of 19.4 years (which I calculated to be 232 monthly payments, rounding down).  Trying to figure out where I am off...

If I use 1.83% for the interest rate and the 2019 applicable mortality table if get

Life only 67 APR = 193.6753 and J&S 100% 67/67 APR = 234.5624

So $125K balance rounded to the dollar gives $645 and $533 which matches DOL fact sheet

Ok, pretend I am a 4th grader....what is the mathematical formula, and the factors used?

26 minutes ago, Gruegen said:

Ok, pretend I am a 4th grader....what is the mathematical formula, and the factors used?

Seriously?

58 minutes ago, Gruegen said:

Ok, pretend I am a 4th grader....what is the mathematical formula, and the factors used?

Using a combination of a mortality assumption, an interest rate assumption, and the participant's age, you can calculate a factor called Annuity Purchase Rate or APR. This is equal to the amount needed to buy an annuity commencing immediately of $1 per month until the participant dies (or in the case of a 100% joint & survivor annuity, $1 per month until the participant and their spouse both die).

The mortality, interest, and age assumptions are all specified in the DOL rule. You should be able to plug those into your software to get the APR. (If you are interested in the math behind the calculation of the APR, be warned you are delving into the realm of actuarial mathematics. I recommend the text Life Contingencies by Jordan. Theory of Interest and Life Contingencies With Pension Applications by Parmenter is also very good.)

Once you determine the APR, divide the account balance by the APR to get the amount of the monthly annuity.