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celia

In another thread, the OP had a question that referenced the Backdoor Roth IRA wiki page.

**I think there is something wrong with the formula shown there**but first want comments from others.

If you convert over multiple years with some non-deductible contributions remaining from a previous year Roth conversion, that appears to not be reflected in this formula. I think the formula should be:C = Amount to Convert to Roth

B = Balances of all pre-tax IRAs

TF = The percentage of the amount you're computing this would be tax-free

TF = 100 * [ C / (C + B)]

What do others say? (Feel free to confirm my math, but that doesn't change my claim that the formula is wrong.)ND = Amount of Non-Deductible dollars in all the non-Roth IRAs, including contributions made for the year

SB = Sum of the Balances of all the non-Roth IRAs at year-end, including the amount converted

TF = The percentage of the amount you're computing that would be tax-free

TF = 100 * ND/SB

For example, assume you contributed $5,000 non-deductible to a new tIRA and already had a pre-tax $15,000 IRA and

*converted $4,000*in the first year. To keep this example simple, suppose there are no more contributions in the following years and no growth. You want to convert half of the remaining IRAs in the second year and the rest in the third year. So $8,000 is projected to be converted in the second and third year.

A.

**Using the current formula gives:**

first year:

TF = 100 * [ C / (C + B)]

TF = 100 * [4,000 / (4,000 + 15,000)] = 21% = $842 of the $4,000 conversion leaving $3,158 to be taxed

That leaves behind $16,000 in the IRAs, of which $4,158 (5,000-842) is basis (non-deductible dollars) and 11,842 is pre-tax.

second year:

TF = 100 * [ C / (C + B)]

TF = 100 * [8,000 / (8,000 + 11,842)] = 40% = $3,225 of the $8,000 conversion leaving $4,775 to be taxed

That leaves behind $8,000 in the IRAs, of which $933 (4,158-3,225) is basis (non-deductible dollars) and $7,067 is pre-tax.

third year:

TF = 100 * [ C / (C + B)]

TF = 100 * [8,000 / (8,000 +7,067)] = 53% = $4,247 of the $8,000 conversion leaving $3,753 to be taxed

But something's wrong since we converted and had untaxed amounts over the three years of $842 + 3,225 + 4,247 = $8,314 when our original basis was only $5,000.

B.

**Using the "new" formula gives:**

first year:

TF = 100 * ND/SB

TF = 100 * 5,000 / 20,000 = 25% = $1,000 of the $4,000 conversion was tax-free leaving $3,000 to be taxed

That leaves behind $16,000 in the IRAs, of which $4,000 (5,000-1,000) is basis (non-deductible dollars) and $12,000 is pre-tax.

second year:

TF = 100 * ND/SB

TF = 100 * 4,000/16,000 = 25% = $2,000 of the $8,000 conversion was tax-free leaving $6,000 to be taxed.

That leaves behind $8,000 in the IRAs, of which $2,000 (4,000-2,000) is basis (non-deductible dollars) and $6,000 is pre-tax.

third year:

TF = 100 * ND/SB

TF = 100 * 2,000/8,000 = 25% = $2,000 of the $8,000 conversion was tax-free leaving $6,000 to be taxed.

In this case, the untaxed amount over the three years is $1,000 + $2,000 + $2,000 = $5,000 which equals the total basis.

The first sentence of the wiki page also references a "nondeductible traditional IRA". There is no such thing. The

*contribution*is deductible or nondeductible, not the IRA. (The term is also implied in the section titled "Mechanics".)