How to calculate earnings of recharacterization from Roth back to regular IRA. The formula my advisor's firm uses makes no sense?

[BAGEL2]

On 1/16/17 I converted $40,000 from my regular IRA to my Roth. On 1/29/18, I recharacterized $25,000 of it back to regular IRA. It was in Roth 378 days. It was invested in CDs earning around 1.5%. The earnings, using that premise, that would need to be returned along with the $25,000 is $388. There were other investments in the Roth. The formula my investment advisor's firm used came up with a figure of $6817 for the earnings  on the $25,000 for those 378 days. There were no other deposits or withdrawls into or out of the Roth. My research found a formula to calculate interest which basically is: the closing balance of Roth prior to recharacterization less the opening balance of Roth including the original $40,000 conversion divided by the opening balance. Since the other assets in the Roth during the period were some mutual funds which appreciated, that formula resulted in $1,082 of earnings based on the 4.32% return. My advisor's firm contends that the "adjusted" opening balance (adjusted for all other ins and outs of which there were none) is the balance prior to the $40,000 conversion and the adjustment is only the $25,000 recharacterization and not the $40,000 conversion. The actual figures are: value of Roth prior to conversion is $40,786; the conversion is $40,000 and the value prior to $25,000 recharacterization is $81,162. Am I wrong? You can contact me directly at [email address removed]. Thanks.

[fanfare]

as I understand it earnings are calculated proportionally, that is period earnings x ( 25,000 / total ROTH IRA value ). If you had mutual funds in there that rose substantially, then that gain is counted partially as earnings.
Yes, only the earnings on the $25,000 would go back to the Traditional IRA.

The earnings don't get reported on your return, only the nominal amount ($25,000).

[dmertz · Accepted solution]

If the value of the Roth IRA was $40,786 immediately prior to the $40,000 Roth conversion into this account (resulting in a value immediately after the conversion of $80,786) your adjusted opening balance is $80,786.  With and adjusted closing balance of the Roth IRA of $81,162 immediately prior to the recharacterization distribution:

$81,162 / $80,786 = 1.00465427 or a gain of 0.465427%

The calculation listed in CFR 1.408-11 is simply a rearrangement of the above:

($81,612 - $80,786) / $80,786 = 0.465427%

0.465427% * $25,000 = $116.36 of gain attributable to the $25,000 being returned.