Line 7 ("Applicable Figure") on (IRS) form 8962 ("Premium Tax Credit") comes from a table in the form's instructions. The table has 167 entries, one for each 1% step in the MAGI/FPL ratio.
If I plot this table (x = MAGI/FPL, y = "Applicable Figure"), it is a curve. The best fit I've come up with is either a 3rd-order polynomial (1) or a logrithmic (2) function. Both are 'close enough', in an engineering sense, but deviate from the specified "applicable figure" by as much as 5 places. (eg, a value of 0.0629, instead of
0.0634)This would not be a big deal as far as calculation; but, (a) they do want the value entered on line 7, so the wrong value could be problematic; and (b), more significantly, I just wonder how the table was generated in the first place.
ISTM, they would pick the end points, choose some mathematical function whose shape fit their fancy, and then just write the table values that the function computed. That does not seem to be the case.
I would appreciate hearing any insights or speculation on this.
NB: my equations are ...
(1) y = (-8.5159 + 12.0268*x - 2.9509*x^2 + 0.3146*x^3)/100
(2) y = (7.9908*LN(x) + 0.7212)/100
... where x = (MAGI/FPL)/100 (IOW, 1.33 - 3.00, over a table span of
133 - 300)