I can see why this is complicated because of the way TurboTax might do 2017.
Treating all contributions as nondeductible:
2015 Form 8606:
Line 1 = $5,440
Line 2 = $0
Lines 3 and 5 = $5,440
Line 6* = $0
Lines 8* and 9* = $5,407
Line 10* = 1.000
Lines 11* and 13 = $5,407
Line 14 = $33
Line 15c = $0
Line 16 and 17 = $5407
Line 18 = $0
* calculation probably done on a separate worksheet by TurboTax but the result is the same
The unrecoverable $33 of basis probably reported as a miscellaneous deduction on Schedule A reducing the basis to zero, but likely less than 2% of AGI so the deduction provides no benefit. Basis to carry over to 2016 is $0.
2016 Form 8606:
Line 1 = $1,400
Line 2 = $0
Lines 3 and 14 = $4,700
2017 Form 8606 (the method I prefer since you don't need to figure your modified AGI to know that your entire IRA contribution is nondeductible)
Line 1 = $5,500
Line 2 = $4,700
Line 3 = $10,200
Line 4 = $2,500
Line 5 = $7,700
Line 6 = $3,047
Line 8 = $4,900
Line 9 = $7,947
Line 10 = 0.969
Lines 11 and 13 = $4,748
Line 14 = $5,452
Line 15c = 0
Line 16 = $4,900
Line 17 = $4,749
Line 18 = $152
However, because there was a nondeductible contribution for 2017 a distribution (conversion) was also done in 2017, TurboTax does the ratio calculation on a separate worksheet under the assumption that you need to use the worksheet because you do not know how much of your IRA contribution is deductible, resulting in the entire conversion coming from basis:
Line 1 = $5,500
Line 2 = $4,700
Line 3 = $10,200
Line 4 = $2,500
Line 5 = $7,700
Lines 11 and 13 = $4,900
Line 14 = $5,300
Line 15c = 0
Line 16 = $4,900
Line 17 = $4,900
Line 18 = $0
2018 Form 8606
Line 1 = $5,500
Line 2 = $5,452 or $5,300 depending on which way 2017 was done
Lines 3 and 14 = $10,952 or $10,800 depending on which way 2017 was done
2019 Form 8606
Line 1 = $6,000
Line 2 = $10,952 or $10,800
Line 3 = $16,952 or $16,800
Line 4 = $0
Line 5 = $16,952 or $16,800
Line 6 = $0
Lines 8 and 9 = $18,066 (current value)
Line 10 = about 0.930 but the actual value doesn't really matter since you are converting the entire balance
Lines 11 and 13 = $16,952 or $16,800
Line 15c = $0
Line 16 = $18,066 (current value)
Line 17 = $16,952 or $16,800
Line 18 = $1,114 or $1,266
From 2016 through 2019 you will have contributed $21,700 and converted $22,966 resulting in a taxable amount between 2017 and 2018 totaling $1,266.
Regarding the calculation for 2017, TurboTax is using Worksheet 1-1 in IRS Pub 590-B:
https://www.irs.gov/pub/irs-pdf/p590b.pdf
If you choose to file 2017 Form 8606 as prepared by TurboTax using the worksheet, I would probably include a copy of the worksheet prepared by TurboTax.
