How much should I put in an IRA to go into the lower tax bracket?

[mrg0834]

My total taxable income is $39,667

[hbl3973]

Referring to the IRS 2016 income tax brackets web page

https://www.irs.com/articles/2016-federal-tax-rates-personal-exemptions-and-standard-deductions

if you are filing as a single person or married filing separately would want to reduce your income by $2,017 to bring it down to to the 15% marginal tax bracket.  If you are married filing jointly or filing as head of household, you cannot reach a lower tax bracket even contributing the maximum $5,500 ($6,500 if 50 years old or older) per person.

All that said, the main objective of contributing to either a traditional or a Roth IRA is to move you along the road to a comfortable retirement income.  IRAs help by providing tax deferred growth, permitting the account to quite possibly double or triple compared to putting the money into the same investments under a regular taxable brokerage or bank CD account.